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AN 

EASY INTRODUCTION 

TO 

ASTRONOMY 

FOR 

YOUNG GENTLEMEN AND LADIES: 

DESCRIBING 

The Figure, Motions, and Dimensions of the Earth; the dif- 
ferent Seasons; Gravity and Light; the Solar System ; tm; 
Transit of Venus, and its Use in Astronomy; tljjr Moon's 
Motion and Phases ; the Eclipses of the Sun and Moon ; the 
Cause of the Ebbing and Flowing of the Sea, See. 



BY JxlMES FERGUSON, F. 



/• »v5» 






SECOND AMERICAN, 

" ROM THE SEVENTH LONDON EDITION* 



ILLUSTRATED WITH CO PPERP L ATE'S- 

>:o:< 



PHILADELPHIA, \^ 

PUBLISHED BY JOHNSON AND WARNERTStffi i -*. f 

HIGH-STREET. 

AttN COCKRAN, PRINTER. 

1812, 
& 



/ 






■ t 








AD PERTISEMEHT. 



THE design of the following Treatise is to 
shew, that Young Gentlemen and Ladies may ac- 
quire a competent knowledge of Astronomy, 
without any previous knowledge of Geometry or 
Mathematics. How far the Author has suc- 
ceeded in this, is left to the judgment and deci- 
sion of his impartial Readers ; to whom, if his 
labours be agreeable and instructive, the nurnose 
for which he wrote will be fully answered. 



CONTENTS. 



Dialogue Pa^e 

I. ON the Motion^ Figure* ana* Dimensions 

fif the Earth - 5 

II. On the Balance of Mature, and the Solar 

System - « - - - 26 

III, On Gravity and Light - - - 46 

I\ r . Ou the Transit of Venus, June 6, 17.61 ; 
and hotv the Distances of the Planets 
from the Sun ivere found thereby 66 

V. On the Method of finding the Latitudes 

and Longitudes of Places -- - 79 

Vim On th e Ca uses of the diffe rent Lengths of 
Days and Nights, the Vicissitudes of 
Seasons, and the various Phases of 
the Moon - - - - 97 

YI'I* On the Moon*s Matron round the Earth 
and Sun. and the Eclipses of the Sun 
and Moon - - - - 115 

VIII. On the Cause of the Ebbing and Floiving 

of the Sea - - - • 135 

IX. On the Fixed Stars, and Solar and Syde- 

rtal Time - - - - 150 

X. On the Projection of Solar Eclifises : To 
i$hich are subjoined, Answers to some 
Astronomical Questions - - 157 



THE 

YOUNG GENTLEMAN AND LADY'S 

ASTRONOMY. 

DIALOGUE I* 

ON THE MOTION, FIGURE, AND DIMENSIONS OJ? 

THE EARTH. 



Neander. GOOD-MORROW, sister; this is 

an early visit I have thought, for these few 

days since I came home, that >ou are anxious 
about something or other. Pray, may I ask 
what it is ? 

Eudosia. Indeed, brother, I am,....but am al- 
most afraid to tell you what it is. 

N. Then you must think me much changed 
since I went to Cambridge. You know I always 

A 2 



6 

ed and esteemed you, on account of the good? 
ness of your heart, which shone forth with the 
greatest lustre in the whole of your deportment* 
....I am still the same as before, excepting the 
improvement I have made at that famous univer- 
sity ; where, not only the sublime sciences are 
taught by the greatest masters, but the truths of 
the Christian religion proved in the lectures which 
I have constantly attended... ..You know that you 
and I used to converse familiarly before I went 
thither : let us do so still. 

E. Dear brother, I cannct express how much 

you oblige me by this behaviour I was afraid 

before to tell you my mind ; but now I will, espe- 
cially as you are to be here for some considerable 
time before you set out upon your travels. What 
I want to learn of you cannot be done, I believe, 
without taking up a great deal of your time ; and 
perhaps you may think me too vain, in wanting 
to know what the bulk of mankind think our sex 
have no business with. 

N. Pray, Eudosia, what is that? 

E. It is nothing less than to be in some mea- 
sure acquainted with the sublime science of As- 
tronomy ; for I have been told, that of all others, 
it is the best for enlarging our minds, and filling 
them with the most noble ideas of the Great Cre- 
ator and his works ; and consequently of drawing 
us nearer to him, with an humble sense of our own 
meanness, and of every thing that the greatest 

X of man can perform* 



N. Indeed, sister, whoever told you so, told you 
a great truth ; and I am very glad to find you have 
an inclination to learn the most sublime science 
that ever was taught by mankind. 

E. But shall I not be laughed at for attempting 
to learn what men say is fit only for men to know ? 

N. Never, by any man who thinks right; and 
I hope you are above minding what those say who 
think wrong. 

E. Now let me speak freely.., ..I have been 
told, astronomers pretend that the sun stands still, 
and that the earth turns round. What do you 
say to this ?....! know you honour the Bible, and 
it asserts the contrary. Now, I see so many things 
in that Book which appear to me to be above all 
the powers of human composition, and carry such 
evident marks of Divinity with them, as are suf- 
ficient to convince me that they could proceed 
from none but God : and therefore I had much 
rather baulk all my inclinations to learning, than 
learn any thing that would prejudice my mind 
against the Bible. 

N. Dear sister, I admire the goodness of your 
heart... .You may depend upon it, that the study of 
astronomy will never have the least tendency to- 
wards prejudicing your mind against the Scrip- 
tures... .You know that we cannot take every thing 
there in the strict literal sense. If we did, we should 
believe that our Saviour was actually a vine at one 
time, a door at another, and at a third time a lamb, 
The Scriptures were given us to teach us what we 



8 

should believe, and how we should behave, in or- 
der to attain and secure to ourselves the favour of 
our Maker here, and our perpetual felicity here- 
after ; which are things infinitely more interesting 
to us than all other knowledge and wealth in the 
world. ...They speak according 10 the common 
apprehensions of mankind, in those points which 
are merely speculative, and have no direct tend- 
ency to influence our morals ; and as they never 
were intended to instruct us in experimental phi- 
losophy, or astronomy, or in any thing else that we 
could acquire by our own industry without them, 
nothing that regards these sciences can either be 
.deduced cr inferred from them.... One might 
with as good reason take up a law-book, and ex- 
pect to find a system of geography in it, as take 
up the Bible with a view to find a system of as- 
tronomy therein. 

E. What you have said is rational and just; 
and now, if you please, I should be glad to enter 

upon our intended subject If the sun does not 

move, pray, to what is he fixed? and what hinders 
him from falling dawn to the earth, when he is so 
high above it, especially at noon in summer ? 

iV. High and low are only relative terms ; for, 
when the sun is at his lowest depression with re- 
spect to us, he is directly over-head to some other 
part of the earth ; for the earth is round like a 
globe, and on whatever part of its surface a person 
stands upright, he thinks himself to be oa the up- 
permost side, and wonders how any one can stand 



9 

Irectly opposite to him, on the undermost side 
of the earth : or rather, how he can hang to it 
with his head downward^ and not fall off to the 
lower sky. 

E, That is what I have often wondered at, 
when I have heard it affirmed that the earth is 
habitable on all sides ; or that, where towns can- 
not be built, ships may sail. How comes it to 
puss, that the weight of a ship causeth it not to 
fall off from the lower seas ; or that these ships 
and seas do not fall off to the lower sky alto- 
gether ? 

N* What we call xveight is caused by attraction* 
....The earth attracts all bodies on or near its sur- 
face towards its centre, equally on all sides, every 
particle of matter alike ; and therefore those bo- 
dies which contain the greatest number of parti- 
cles of matter, acquire from this attraction the 
greatest and most forcible pressure ; and conse- 
quently have (what we call; the greatest weight...* 
The earth may be compared to a great round load- 
stone rolled in filings of iron, which attracts 
equally on all sides ; so that they cannot fall off 
even from its undermost side : nay, it will take 
them up from a table, if they be within the sphere 
of its attraction.. ..By and by, you shall be satis- 
lied with respect to your query about the sun. 

E. So far I understand you very well ; but still 
it seems odd to me, that people should stand op«« 
posite to us on the earth, with their heads down*- 
ward* 



10 

N. I believe it does ; but you know, that ei- 
ther the sun must go round the earth to give us 
Jays and nights, or the earth must turn round 
like a globe on its axis to do so ; and will not ei- 
ther of these motions answer the intended pur- 
pose ? 

E. Undoubtedly it will. 

M Now, as I have no mind to deceive you, 
and shall in due time prove every thing that I ad- 
vance, even to your own satisfaction ; I do say, 
that the sun does not move round the earth every 
twenty-four hours, but that the earth turns round 
in twenty-four hours : and as the sun can only en- 
lighten one half of the earth at any given instant 
of time, and the other half must then be in the 
dark ; this motion of the earth will cause the dif- 
ferent places on its surface to revolve through the 
light and the dark in twenty-four hours ; in which 
time of course, they must, have a day and a night: 
and at the instant when it is mid-day at one place 
it must be midnight at the, opposite.. ..Do you be- 
lieve what I say with respect to the earth's turn- 
ing round ? 

E. I do, because I am fully satisfied that you 
would not willingly deceive me ; and you have 
promised to prove that it does. 

A r . Then, be pleased to stand up for a minuted 
*...It is now seven o'clock it the morning, and you 
think you are standing upright, on the uppermost 
side of the earth.. ..You will think the same if you 
stand upright at seven o'clock in the evening, when 



11 

the earth has turned half round, because you will 
then perceive no difference of posture : and yet, at 
that time, you will be very nearly in the same po- 
sition as a person is just now, who stands on the 
side of the earth opposite to us, which person be- 
ing as strongly attracted by the earth there, to- 
wards its centre, as we are here, he is in no more 
danger of falling off downward, than we are at 
present of falling upward. 

E. Pardon me, sir ; if you had not been at the 
university, I should have thought falling upward 
a very improper expression. 

N. So it is ; and 1 do assure you that I never 
heard such an expression at the university, nor 
do I ever remember to have used it before. ...But 
to proceed. 

Up and doxvn are only relative terms. Let us be 
on what part of the earth we will, we call it up to- 
ward the sky over our heads ; and down toward the 
centre of the earth, to which all terrestrial bodies 
would fall, by the power of the earth's attraction. 
So that, with regard to open space, what is up from 
any given point of the earth's surface, is down from 
the opposite point thereof. And as the sky sur- 
rounds the whole earth, we call it up toward the 
sky over our heads, be where we v/ill ; and down 
from our place toward the centre of the earth. 

E. Then, to be sure, we can perceive no differ- 
ence, as to our position at different times of the day. 
You have quite satisfied me in this : but pray, how 
can the earth move, and we not feci its motion ? 



12 

N. I heard you was at Plymouth last year ; had 
you not then the curiosity to go aboard some ot 
the ships there, or at the Dock ? 

E. My papa and I went to the Dock, with a 
small party of gentlemen and ladies. Mr. Fal- 
coner, who was then master of the Belleisle, hap- 
pened to be on shore ; and observing that we were 
strangers, he most politely invited us to see his 
ship, which was then lying with many others in 
the Hamoaze. We most willingly accepted his 
invitation, and he took us all out in his boat; 
shewed us first into the cabin of the ship, and, as 
it was in the afternoon, he genteelly treated the 
gentlemen with wine, and the ladies with tea ; af- 
ter which, he shewed us the whole inside of his 
ship of war. The way that the different apart- 
ments are laid out, especially the powder-maga- 
zine, and how it is secured from being dangerous ; 
the method of steering the helm, and many other 
things which I cannot well remember, was a sight 
not only highly entertaining, but greatly surprising ; 
and I could not help wondering how it was pos- 
sible for the art of man to contrive and build such 
a wondrous huge machine, and how it could be 
managed and conducted through the pathless 
seas. 

N. It is surprising indeed ! but how infinitely 
more so is the power and skill of the Great Crea- 
tor of the universe, who has made such prodigious 
bodies as the planets of our system are (one of 
which is a thousand times as big as our earth,) 



1 



a 



and has set them off in the trackless space around 
us, with such degrees of swiftness as you will be 
amazed to hear of ; and yet, at the end of each 
circuit, they begin the same over again, at the 
same parts of space from which he set them off at 
first..... And the disposition of all the apartments 
of the ship will not dare to be compared, not only 
with the structure of the human body, but even 
with that of the meanest animal on earth. ....Was 
the day calm or windy ? 

E. Scarce a breath of wind was stirring : the 
sun shone clear, which made the surface of the 
water around us have a very pleasing aspect : and 
the sight of the ships about us, and of the town, 
was a most beautiful prospect. 

N. I suppose you looked out through the cabin 
windows whilst you were at tea.... Did you see the 
same objects all the while ? 

E. I looked out very often ; the first object I 
saw was a large house in the Dock-town ; but it 
seemed to me as if it moved very slowly towards 
the right hand. I soon lost sight of it, and other 
objects appeared to my view, and disappeared 
slowly and gradually; which could arise from no 
other cause than the very slow and gentle turning 
of the ship the contrary way. 

N. True ; but did you feel the motion of the 
ship ? 

-E. Not in the least ; and the whole company 
agreed, that if we had not looked out, we should 






not have thought that the ship had any motion at 
£hat time. 

N. And is not that single case sufficient to con- 
vince you, that the earth may turn round, and car- 
ry us all about with it, and we feel nothing of its 
motion ? especially as the motion of the earth is 
much more regular and uniform than the motion 
of a ship, or any other machine that human art can 
contrive. 

E. I confess it is.*..But if the earth turns round, 
how comes it to pass that a stone thrown directly 
upward, falls down again, upon the very same 
place of the earth from which it was thrown up..... 
For, considering how large a globe the tarth is 
the parts of its surface must move very fast, to 
turn round once every twenty-four hours. And 
if it turns at all, its motion must be eastward ; be- 
cause the sun, moon, and stars, appear to move 
from East to West. Now, I should imagine, 
that a stone or ball thrown directly upward from 
any place, would fall as far to the westward of that 
place, as the place itself has got to the eastward, 
whilst the stone was disengaged from the earth, 
and rising and falling in the same line. 

N. Your observation is very sensible.... But you 
ought to consider, that any body which is put into 
motion will persevere in that motion till some- 
thing or other turns it aside, or stops its course. 
The stone partook of the earth's motion before it 
was disengaged therefrom : the person who took 



15 

it up had the same motion, by which means it was 
still communicated to the stone ; and therefore 
its motion was as quick eastward while it was 
rising and falling in the open air, as the earth's 
motion is ; so that it could not miss falling down 
again upon the same part of the earth. And al- 
though it would have appeared to a spectator to 
ascend and descend in the same perpendicular 
line, yet its real motion was in a curve, and would 
manifestly have appeared so to an observer at rest 
in the open air, on whom the earth's motion had 
no effect. 

If a large boat was sailing along near t 
shore, two persons opposite to one another in the 
boat might toss a ball to each other, over and over 
across the boat, to catch for their diversion, and 
they would imagine it to be only going to and 
fro, from one person to the opposite, always in 
the same line ; whereas it is certain, that the pro- 
gressive motion of the ball, going from one side 
to the other, would be equal to the progressive 
motion of the boat ; for if it were not, the oppo- 
site person (who had a progressive motion) could 
not catch it. And although it would appear to 
all the people in the boat, to move forward and 
backward in the same line, yet, to an observer on. 
the shore, who is no way affected by the motion 
of the boat, the bail would be seen to have a zig- 
zag motion, never returning to either person in 
the same line in which he tossed it toward the 
other, 



16 

£• You have j convi me, that ther: 

nothing conclusive In my argut: against the 

eaith s motion.. ..And, in confirmation of what you 
said about a body's being put in motion, that it 

ill naturally persevere therein, till some cause or 
other turns it aside, or stops its course, I had once 
the experience thereof; and very painful it was. 
For crossing our river in the boat, I stood up 
when it was about half way over; and as its mo- 
tion was uniform by the men pulling the rope, I 
was quite insensible both of its motion and my 
own. But when it stopt suddenly against the bank 
of the river, I fell forward on my face, and was 
much hurt by the fail. Whereas, if I had not, 
without knowing any thing of the matter, naturally 
persevered in the motion given me by the boat, I 
could not have fallen when it was stopt. 

If. Indeed, Eudosia, you have given a true 
philosophical account of the cause of your falling: 
and now, I think, we may, for the present, have 
done talking of this matter. 

E. I think so too; for, speaking of the fall makes 
me almost imagine I still feel it.. -.But, pray, how 
do you prove that the earth is round like a globe? 

Ni I will prove that immediately. The sun 
shines in through the window.... 

E. What then ? 

N* Have patience a minute, and look at this 
small globe in my hand, and the flat circular plate 
that lies on the table. ....You see the globe may be 
hung by the thread which is fastened to it. I now 



17 

twist the thread, and hang the globe by it in the 
beams of the sun ; and the globe casts a shadow on 
that upright board behind it. You see that the 
globe turns by the untwisting of the thread ; but 
let it turn how it will, it always casts as round a 
shadow on the board as if it did not turn at all.... 
I now fix a thread to the edge of the flat circular 
plate, and hang the plate by the thread a little twist- 
ed. You see, that when the broad-side of the plate 
faces the sun, it casts a round shadow on the board, 
as the globe did : but as it turns obliquely toward 
the sun, by the untwisting of the thread, its sha- 
dow is of an oval figure on the board ; and when 
its edge is turned toward the sun, its shadow on 
the board is only a narrow straight line. 

E. All this is plain ; but I cannot imagine what 
you are to infer from it. 

N. The earth always casts a shadow toward 
that part of the heaven which is opposite to the 
sun ; and the moon appears as fiat to us as the 
board on which the shadow of the small globe was 
projected. When the earth's shadow falls upon 
the moon, we say, the moon is eclipsed. These 
eclipses happen at all different times of the twenty,, 
four hours ; and, consequently, when all the dif- 
ferent sides of the earth are successively turned 
toward the sun. But the earth's shadow on the 
moon is always bounded by a circular line ; and 
therefore it is plain, that the earth must be of a 
globular shape.... For, if it were shaped like this 
flat circular plate, its shadow on the mQon could 



18 

never be circular but when its broad-side was turn- 
ed directly towards the sun. At other times, the 
shadow would be either of an oval figure, or only 
a straight line, as you have seen on the board. 
There are several other ways of proving that the 
earth is round ; but I believe you are satisfied, 
that it is so, from what I have now shewn you. 

£• I am entirely satisfied, and therefore more 
proofs would be superfluous. But I should 
now be glad to know how you prove that the 
earth turns round ; and that the sun does not go 
round the earth. 

A T . Before I proceed to the demonstration, I 
Will ask you a very plain question, which I hope 
you will not take amiss, as I have not the least 
design to affront you. 

E. Indeed I do not believe you have ; and 
therefore I beg.you w T ill ask it. 

N* Suppose you put a small bird on a spit, and 
put it to the fire ; whether is it the best way to turn. 
the spit round with the bird, or to let the spit stand 
still, and move the fire round about it ? 

E. Your question almost surprises me.. ..for not 
to speak of the wisdom of man, sure no xvoman of 
common sense could be so absurd, as to set about 
contriving how to make the large fire and grate 
be carried round the spit. 

A. True, Eudosia Now I can assure you, 

that the sun is at least a million of times as big as 
the earth ; and is therefore more unfit to be moved 
round the earth, than a great fire, and the grate 



19 

that holds it, is to be moved round a small bird 
on a spit.. ..And as no man in his senses would go 
to work on such an absurd attempt, would it not 
be horrid blasphemy to suppose that the DEITY,, 
who is the very essence of wisdom and perfection, 
would do so ? 

£. Heaven forbid the thought! the bare men- 
tioning such a thing is enough to chill one's blood. 
•...Were I sure, that the sun could be proved to 
be a million of times as big as the earth, I should 
ask no farther demonstration of the stability of the 
sun and the motion of the earth; because I should 
naturally conclude, that the sun is a million of 
times more unfit to move than the earth is. And 9 
as the most superlative degree of wisdom and rea- 
son is in the Deity, it is impossible for me to 
imagine he could do any thing that is irrational. 

My belief is, that he always makes use of the 

fewest, most simple, and most rational means, to 
produce the greatest, most noble, and most as* 
tonishing effects ; such as his infinite goodness 
and beneficence to his creatures has rendered 
conducive to their welfare, in numberless in- 
stances. 

N. He certainly does.... And now I will prove 
to you, that the earth turns round every twenty- 
four hours ; not upon any material axis, but on 
an imaginary straight line within itself, passing 
through its center, and terminating in its North 
and South points, which are called its North and 
South Poles; as an orange would turn round in 



20 

the open air, if you first set it a whirling, and 
then throw it off your hand, in the air. 

Water naturally runs downward, all around the 
earth, from these parts which are highest, or far- 
thest from the center, towards those which are 
lowest, or nearest to it : and this is caused by the 
power of the earth's central attraction, which 
draws the water and all other bodies that way. 
Now, if the earth was perfectly round and smooth 
like a polished globe, all the parts of its surface 
would be equidistant from its center, and water 
could never run upon it. About three-fourth 
parts of the earth's surface is covered with the 
seas, which join or communicate with each other. 
And if the earth had no motion round its axis or 
center, the attractive force (which is equal all 
around at equal distances from the center) would 
cause the surface of the seas to be of a perfectly 
round and globular form. 

E. Undoubtedly it would : for then, as every 
particle of the water's surface would be drawn with 
equal force towards the earth's center, and these 
particles do touch each other; none of them could 
get nearer the center than their neighbouring 
ones. 

N. Right.... And now, supposing the earth to be 
at rest, and the surface of the oceans and seas to 
be perfectly globular, what do you think the con- 
sequence would be, if the earth should begin, and 
continue to turn round on a line within itself, as 
if ij turned on a real axis. 



21 

£. Let me think a little.... I have observed, that 
"when our maid took her mop out of a pail of wa- 
ter, the head of the mop was round ; but when 
she began to trundle it on her arm, it immediate- 
ly became flattened at the parts of the stick which 
were even with its surface ; and it swelled out in 
the middle..... Pray, brother, if I may be allowed 
to make a very odd sort of a comparison, may not 
an imaginary line in the heart of that part of the 
stick which is within the mop be called the axis 
round which the mop turns ; as you have told me 
that such a line within the earth, from its North 
to its South poles, is called the axis of the earth ? 
.....If so, seeing that the waters on the earth are 
of as yielding a nature as the cotton of the mop, I 
apprehend, that if the earth turned round its axis, 
the surface of the seas about the poles would be- 
come flat, and the surface of the seas which are 
farthest from the poles would "swell out, all around ; 
and so, the figure of the earth would be like that 
of a whirling mnp. 

N. No philosopher could have made a more apt 
comparison, nor have drawn a better conclusion 
from it. V* hen I told you before, that the earth is 
round, I did not mean that it is strictly so ; al- 
though at the distance of the moon, it would ap- 
pear to be round, as its shadow on the moon does 
to us. I do not here consider the hills, as anything, 
because they are so little in comparison to the 
whole bulk of the earth, that they take off no more 
from its roundness in general, than grains of dust 



22 

do from the roundness of that small three inch 
globe which you see on the table. It is quite round, 
and covered all over with paper, on which there 
is a map of the land and water on the earth's sur- 
face. The middle line (see Fig. 1 of PLATE I.) 
or circle, that is drawn round it, is called the 
Equator, which divides the globe into two equal 
parts, called the Northern and Southern Hemis- 
pheres, or half globes. The North and South Poles 
are the middfc points of the North and South he- 
mispheres, each pole being a quarter of a circle 
distant from each point of the equator, all around'- 
and a straight line drawn through the center from 
pole to pole, is called the axis of the globe. 

If the thin papers were scraped off from the 
poles and almost half wav round them toward the 
equator, the globe would be a little flattened at 
the poles, and comparatively so much swelled out 
about the equator ; but if it were then viewed 
from the distance of six or seven feet, it would 
•still appear to be round. 

E. I believe it would ;....but what of all this ? 

N. From actual measurement arid observation? 
the earth is proved to be a little flattened at the 
poles and swelled out about the equator -, the equa- 
torial diameter of the earth being thirty- five miles 
longer than the axis or polar diameter. This you 
may think a great deal, but it is very little when 
compared with the bulk of the earth, as you will 
easily judge when I tell you, that no less than 
25,000 English miles would measure it round, and 
the highest mountains that are known are not 




Gv&ylUToaaSc, 




£i'.l vie /'•></«<'<'. 






a 



3 



three miles of perpendicular height.o.«.««"Now ? 
as water naturally runs downward, if the earth 
had no motion on its axis to keep up its figure, 
the water of the seas would run from the higher 
parts about the equator, to the lower parts about 
the poles, and overflow the polar region? for 
many hundred miles all around ; and even Britain 
itself would be laid several miles under water. 

E. This is a very plain case and the not return- 
ing of the waters from the seas about the equator, 
is to me an evident proof of the earth's turning- 
round its axis ; without which, the surface of the 
waters would become of a general roundness, as I 
saw the head of the mop do when the maid left 

off trundling it And now it seems plain that the 

Almighty must have made the rigid earth as much 
higher about the equator, than the land is about 
those places near the poles, as the earth's quick 
motion about the equatorial parts would cause 
the waters to rise there. For I see by the globe, 
that there are great quantities of land about the 
equator, and many small islands in the seas which 
are not overflowed. 

A r . The more you know about these matters, 
Eudosia, still the greater reason you will have to 
admire the power, and adore the wisdom and 
goodness of the Deity, 

E. Indeed, brother, I believe I shall.. -.And I 
already begin to think that if an atheist would be 
persuaded to learn Astronomy, it would soon 
cure him of his infidelity. 



24 



to So I have often thought since I knew any 
thing of the matter. 

E. I think you told me, that almost three-fourth 
parts of the surface of the earth is covered with 
seas; and by looking on that small globe, I imagine 
it may be so. But you have not yet told me, 
how rt is known, that the earth's circumference is 
twenty-five thousand English miles; and perhaps 
I should not be able to understand it if you did. 

to The bulk of the earth is ascertained by 
(what is called) Geometry, and could not have 
been known by any other kind of learning. And 
as you do not yet understand any part of that 
science, I should only confound your head by 
talking to you on that subject at present. 

E. Your saying, « at present » gives me some 
hopes, that you will endeavour to instruct me in 

that branch of science afterward But can 

you tell me just now, how many miles of the 
earth is land, and how many are covered with 
the seas ? 

to. The surface of the earthy part of our 
great globe is divided into four great tracks 
or spaces, called Europe, Asia, Africa, and Ameri- 
ca, as you see them laid out. on the small three 
inch globe. 

According to measurement of the best maps, 
the seas and unknown parts of land contain 
1< 0,522,025 square miles; the inhabited parts 
38,990,569; Europe 4,456,065 ; Asia 10 768,823 ; 
Africa 9,654,80/; America 14,110,874. In all 






199,512,595 J which is the number of square 
miles on the whole surface of our globe. 

E. I admire the prodigious bulk of the earth ; 
but infinitely more so the power that must have 
set it in motion at first. 

N. Nothing is great or small but in comparison, 
We are very big when compared with animals 
which can be seen only by the help of a microscope: 
the earth is big indeed when compared with our- 
selves, who live upon it ; the planet Jupiter is a 
thousand times as big as our earth, and the sun is 

more than a thousand times as big as Jupiter 

If you so justly admire the power that put our 
small planet the earth into motion, how much 
more must you admire the power which put the 
whole planetary system round us in motion ! 

E* I sink into nothing, in my own mind. Alas, 
what have we to be proud of? If I had been proud 
before, Astronomy would have cured me effectu- 
ally of it. 

iV. Indeed it might cure any one of pride : and 
I believe no astronomer can be either proud or 
impious. But hark !.... the bell rings for break- 
fast ; I thought to have satisfied your query about 
the sun, but must leave it till the next opportunity. 
Be sure then to put me in mind of it, and after- 
wards to talk about the solar system. 

E. I believe I shall have no occasion to remind 
you. 






DIALOGUE II. 

OS THE BALANCE OF NATURE AND THE SOLA I* 

SYSTEM. 



Ntander* WELL, sister; what became of you 
yesterday after breakfast? I went to my room im- 
mediately after, thinking you would follow me, 
that we might have a little conversation. But, in- 
stead of that, you have left me quite alone ; for I 
never saw you the whole day afterward, except at 
dinner and supper. 

EudoSia. Indeed, brother, I was so much pleased 
with what you told me yesterday morning, that I 
was willing to make the most and best of it that 
I could ; and therefore employed the rest of my 
time in writing down every thing that I could re- 
members 

N. I am very glad of it ; and now I find you in- 
tend to emulate a young lady of quality ; who, last 
year, attended a course of lectures on experiment- 
al philosophy at Tunbridge Wells ; and always 
when she went home, wrote down what she had 
heard and seen. The person who read the lectures 
informed me, that he was (though with some diffi- 
culty) favoured with a sight of the young lady's 



manuscript ; and assured me, that she had therein 
given a very good account of the machineiy and 
experiments. I hope you will not refuse to shew 
me yours, every day, as you proceed. 

E. You shall always see it, were it only for this 
selfish reason, that you may correct and amend 
what is wrong in it ; and then I shall reap the 
advantage, I will now repeat my yesterday's 
query : To what is the sun fixed ? for you have 
convinced me that he does not move round the 
earth. 

iV. The sun is not fixed to any thing at all ; nor 
is it any way requisite he should. I told you that 
the falling of bodies to the earth is solely caused 
bv the earth T s attraction. 

E* I remember it very well ; and it seems plain 
to me, that their falling towards the earth's cen- 
ter, on all sides of it, is a demonstrative proof of 
the earth's attraction. For what else could dos- 
sibly determine bodies to foil, on opposite sides 
of the earth, ia directions quite contrary to one 
another ? 

N. Right, Eudosia, you are a philosopher al- 
ready ; and I shall have very great pleasure in 
teaching you, at least the rudiments of Astrono- 
my. 

The tendency of bodies to fall, is called their 
Gravitation, and the power which gives them that 
tendency, is called Attraction* Now, supposing 
the sun (PLATE I. Fig. 2.) to be the only body 
that exists in universal space, and that he is put 



28 

into any part of open space, pray, to what other 
part of space do you think he would fall . ? 

E. I think he could not fall to any other part 
of space at all, because there would be no other 
body to attract him : and therefore, J. imagine, 
that he would always remain where he was placed, 
self balanced on his center; as my favourite poet, 
Milton* elegantly expresses it, concerning the earth. 

N. Your observation is sti icily just. And now, 
to lead you further on, I tell you, that the sun's 
attraction reaches many millions of miles all 
around him j and that all bodies attract each other 
according to their respective quantities of matter; 
that is, according to the number of particles of 
matter they are composed of. I have already told 
you that the sun is a million of times as big as the 
earth : and as the sun and earth are within the 
reach of each other's attraction ; whether do you 
think, that the sun should fall to the earth, or the 
earth to the sun ? 

E. I think, that if the sun contains as much 
more matter than the earth does, as he is bigger 
than the earth, it is a million of times more rea- 
sonable that the earth should fall to the sun, than 
that the sun should fall to the earth. 

X. Right again, sister ; but now I must inform 
you, that the sun is not so compact or dense a 
body as the earth is ; and therefore he doth not 
contain as much more matter than the earth does, 
as he is bigger than the earth. But his quantity 
of matter is more than 200 ; 000 times as great as 



29 

the earth's : and, consequently, he attracts the 
earth more than 200,000 times as strongly as the 
earth attracts him. 

E. Then I should think, that the sun and earth 
would naturally fall toward each other, and come 
together at last : only, that the earth would fall 
200,000 times as fast toward the sun, as the sun 
would toward the earth. 

N. And so they would if there were nothing 
to hinder them. 

E. And what is it that hinders them ? 

N. I will begin to answer your question by ask- 
ing you one Did you ever put a pebble into a 

sling, and whirl it round your head ? 

E. Yes, sir, when I was a child. 

N. And did you feel no tendency in the pebble 
to fly off from the sling. 

E. O yes ! and the moment I let the string slip 
from my hand, away the pebble flew I like- 
wise remember, that the faster I whirled the 
sling, the greater was the tendency of the pebble 
to fly off; and that I was obliged to pull the string 
so much the stronger, to keep the pebble from 
doing so. 

N» That observation will be of more servic© 
to you by and by, than you at present think of i 
but it would be too soon to tell you just now how 
it will. 

E. I will wait till you find it proper to tell me* 

But I am almost impatient to know what you are 

to in/er from the pebble and sling* 

C 2 



so 

2v. All bodies that move in circles have a con- 
stant tendency to fly off from these circles ; which 
tendency is called their centrifugal force. And, in 
order to keep them from flying off, there must be 
an attractive force at the centers of these circles, 
equal to the centrifugal force of the moving bo- 
dies. The earth goes round the sun once a year, 
in an orbit or path which is nearly circular ; and 
it would as naturally fly off from its orbit, if the 
sun did not attract it, as the pebble flew out of 
the orbit that is described round your head, when 
you quitted your hold of the string. 

E. this is new doctrine to me ; for you never 
told me before, that the earth goes round the sun. 
The earth then has two motions, one round its 
axis in twenty-four hours, and one round the sun 
in a year..., Can you prove as clearly that the earth 
goes round the sun, as you have proved that it 
turns round its axis ? 

N. I will prove it negatively just now, and po- 
sitively afterward. If the earth had no motion 
round the sun, it could have no centrifugal force, 
to hinder it from falling to the sun by its owa 
weight or gravitation, which is constituted by the 
power of the sun's attraction. 

E. I see that the earth's motion round the sun 
is indispensably necessary, and am therefore sa- 
tisfied that it does exist. But I think the sua 
would require some motion too, in order to give 
him a centrifugal force ; without which, it seems, 
to me, that big as he is, the earth's attraction 



31 



would pull him out of his place. For, I remem- 
ber that the pebble and sling pulled my hand so 
strongly, although the pebble was small, that I 
could not possibly keep my hand steady whilst 
the pebble was in motion. 

N. Well done, sister The sun really moves 

in an orbit as well as the earth ; and the suns or- 
bit is as much less than the earth's, as his quantity 
of matter is greater than the earth's. And, as 
both these bodies go round their orbits in the 
same period of time, the sun moves as much slow- 
er than the earth does, as his quantity of matter 
is greater than the earth's. So, what is wanting 
in the velocity or swiftness of the sun's motion, is 
. made up by his quantity of matter ; and what is 
wanting in the earth's quantity of matter, is 
made up by the swiftness of its motion in its or- 
bit : on which account their centrifugal forces are 
equal to each others attractions ; and as these at- 
tractions, keep them from flying out of their orbits 
by their centrifugal forces, so these forces keep 
them from falling towards each other by their 
mutual attractions.... -And this is what we call, 
the great balance of nature. 

E. This is a new light to me, and a most delight- 
ful one it is. But, although i think I understand 
it, I wish you would further explain it by a figure. 
N. Here is a figure (PLATE 1. Fig. 3.) which 
I drew last night on purpose for you ; in which 
suppose A to represent the sun, B the earth, and 
C the line of direction in which the sun and eartti 



32- 

mutually attract each other : in which line, take 
a point £•, as much nearer the center of A than the 
center of £, as B contains less matter than A; the 
center of A being at A, and the center of B at i. If 
A and B were allowed to fall against each other, by 
the power of their mutual attractions, then, in the 
lime that A would fall through the space h g, B 
would fall through the space i g ; and both these 
bodies would meet atjf, because B would fall as 
much faster than A, as its quantity of matter (and 
consequently its attractive force) is less than that 

of A* 

But, in the time the small body B goes round the 
large circle a b c, the great body A goes round the 
small circle def; by which motion, each of these 
bodies acquires a centrifugal force equal to the at- 
tractive force of the other ; and the pointy is the> 
center of both the circles which the bodies de- 
scribe ; and is called their common center of gra~ 
vity, or the center of gravity between them. 

E. I should be glad to know why it is so called. 

N. I will tell you, ....Suppose A and B to be two 
balls of different quantities of matter, and conse- 
quently of different weights ; and that those balls 
are connected by a small inflexible wire C, that 
has no weight at all (if you can imagine a wire to 
have no weight, like the immaterial line in which 
the sun and earth attract each other., Hang the 
wire by a thread fixed to the point g^ which 
point is as much nearer the center of the great ball 
A, than it is to the center of the little ball B y as 



33 



the weight of B is less than the weight of At and 

he^hese balls will support and balance each 

oZ like different weights at the two ends of a 

" ,-eelvard by which you have seen meat 
common steeiyaro, u i ■> f _ 

• u i ot home after it was brought irom mar 
weighed at home, anci center or 

ket The point ff may represent the cente 

f -the steelyard, which bears the weights Aftt 
axes of the steeiyaro, as Erav ity and weight 

are at both its ends. And as gra y rf 

are synonimous terms, the point 5, 
the steelyard, is not improperly termed the center 
of gravity of the weights -4 £*f and atn 

E . I understand 7™ P'*^ * have taken 
much obliged to you for the pains >o 
hitherto to make every *£**& ^^ 

\T A«rl now if VGU tWISt Uie Ulicau. j 

t he wife and baUs^ suspended at the pointy the 
the wire and oa r ^ ^ t(j gQ 

bc f„«„ The suu and .he earth is a tnouonkss P o,n,. 

AT. And vour inference is just. 

£ I was jns. going to ask you a quesuon, but 
Jtery gJa fucky thought pr.ven.ed nre , for 

„£ he' hegan ,o teaeh yon French , £*£, 
iut.Hak out, right or wrong: ./!/« are ntcng 1 

lu,L :au S K atyoui ' f' 1 f' ^ZC 
Mil me what your intended question rvas. 



34 

£. As we were obliged to hang the wire and 
balls by a thread, to support their center of gravity ; 
I was just about to ask, what is it that supports 
the center of gravity between the earth and the sun? 

jV. Well:.... And what was the lucky thought 
that prevented your asking that question ? 

E. I immediately recollected, that we must sup- 
port the center of gravity between the two balls, 
because, otherwise they would have fallen to the 
great earth by the power of its attraction. But, 
as there is no greater body than the sun and earth 
to attract them, they could fall no way but toward 
each other; and therefore, the common center of 
gravity between them needs nothing to support it. 

N. If you had asked the question, I should have 
told you the very same thing. 

E. If all the parts of astronomy are as easily 
learnt as those which you have already taught me, 
I shall have no reason to be vain, even if I become 
a tolerable good astronomer by your instructions. 

N. I dare not say they are ; but I will make 
every part of it, which I inform you of, as plain as 
I can. 

E~ You have already told me that the earth is 
a planet, and that there are other planets besides, 
which go round the sun. 

N. Yes : there are five besides our earth : and 
they are called Mercury, Venus Mars, Jupiier, 
and Saturn* 

E. Then ouuun must be their sun too. 

N. It is really so i and enlightens them ail. 



35 



;. I could never believe that the Almighty 
Joes any thing in vain ; and therefore I begin to 
think, that all the other planets are inhabited as 
well as our earth. For, to what purpose could 
the sun shine upon lifeless lumps of matter, <f 
there were no rational creatures upon them to 
enjoy the benefit of his light and heat? 

A r . Ay, why indeed?-.. And I will tell you one 
thing more, which will confirm your belief that they 
are inhabited. They turn round their axes, as our 
earth turns round its axis ; for which plain reason, 
they have days and nights as our earth has : and 
the" two which are farthest from the sun, namely, 
J 'upiter and Saturn, and which, consrquently, have 
much less light than our earth has ; have moons 
to enlighten them, Jupiter four, and Saturn 

five. 

E. To me, this is a positive proof of their being 
inhabited ; and is enough to make us thiinfe, that 
we are but a small part of the creation, or of the fa- 
vourites of Heaven : and that all the regards of 
Providence are not attached to our diminutive 

concerns. 

N. The Divine providence is universal. .GOD 
loves his creatures, as is manifest by what he hath 
done for us, who, perhaps, deserve less of his fa- 
vour than the inhabitants of all the olher planets do 
taken together....It is as easy to him to take care 
of thousands of millions as of one individual and 
to listen to all their various requests .... On account 
t>f his omnipresence, nothing can escape his no^ 



56' 

tke ;~ and on account of his omniscience, nothing 
can escape his knowledge ! 

E. And, as his omnipotence may be inferred 
from his works, so I have often thought that his 
goodness may be inferred from his power* For, 
as he had power enough to make the world, he 
certainly has power enough to punish the world i 
and, consequently, if his goodness w r ere not equal 
to his power, he would punish us severely for 
breaking his laws. 

N. I believe, sister, a more just inference was 
never made. 

E. Do all the planets go round the sun in a 
year, as our earth docs? 

N. No ; those which are nearest the sun, go 
soonest round him 5 and those which are farthest 
from him are longest in performing their circuits. 
E* And do they all move round the center of 
gravity between the sun and them, as round a 
fixed point ? 
A r . They do. 

E. Then, as the times of their going round the 
sun are so various, I cannot see how the sun can 
describe any regular circle round the common 
tenter of gravity between him and them all. For, 
in order that the sun should moVc regularly round 
such a, circle, I think all the planets would need 
to be joined together in one mass. 

N. 'Tis very true ; and we must proceed by de- 
grees. What I shewed you by the figure was 
only on supposition, that there is but one planet 



belonging to the sun* But as there are six be- 
longing to him, and going round him in very dif- 
ferent periods of time, he is only agitated (as it 
were) round the common center of gravity of the 
whole system ; and describes no regular or per* 
feet circle round it, but is sometimes nearer to it 
and at other times farther from it, according as 
he is attracted by a greater or smaller number of 
planets toward any side of the heavens, 

E. In what time do all the planets go round the 
sun? 

.A 7 ". Mercury in 87 days 23 hours of our time ; 
Venus in 224 days 17 hours ; the Earth in S6S 
days 6 hours ; Mars in 685 days 23 hours ; Ju- 
piter in 4332 days 12 hours ; and Saturn in 10,759 
days 7 hours ; all the same way, from West, by 
South, to East. 

E* And do you know what their distances, 
from the sun are ? 

N. Their comparative distances from the sun 

i 

Jiave been known long ago, both by the laws of 
nature, and by observation, and are as follows...* 
If we suppose the earth's distance from the sun 
to be divided into 100,000 equal parts, Mercury's 
distance from the sun will be equal to 38,710 of 
these parts ; Venus's distance 72,333 ; Mars's 
distance 152,369 ; Jupiter's distance £20,096 ; 
and Saturn's distance 954,006. 

£. And can you tell how many miles are con* 
tained in these parts ? 

a 




35 

.A 7 *. Not so exactly as we could wish ; yet astro- 
nomers have come much nearer to the knowledge 
thereof, by the late transit of Venus over the sun, 
on the 6th of June 1761, than ever they were be- 
fore ...•But we must wait with patience till the 
vear 1769, when there will be a much better tran- 
sit of that planet over the sun, in the evening of 
the third of June ; by which means if it be pro- 
perly observed at different places of the earth, the 
dimensions of the whole system will be very 
nicely known, And the astronomers will do well 
to embrace that opportunity, because there will 
not be such another in an hundred years after- 
ward* The method of finding these distances by 
the transit is purely geometrical ; which, as you 
have not yet learned any thing of geometry, I 
cannot at present make you understand* 

E. But, tell iru , whattht-se distances are, as de- 
duced from the late transit in June 176i. 

JV. Mercury's distance from the sun is 
36,841, 4 r 8 English miles : Venus's distance 
68,891 48 -i : the Earth's distance 95,173,127: 
Mars's distance 145 014,148 : Jupiter's distance 
494 990 976 : and Saturn's distance 907,956,130. 

E. These distances are so immensely great 
that I can form no ideas of them. 

A 7 . Then I will endeavour to render them more 
familiar to you. For we are generally so much 
used to speak of thousands and millions, that we 
have almost lost the idea of the numbers they 
contain. 



39 

Suppose a body, projected from the sun, should 
continue to fly at the rate of 480 miles every 
hour (which is much about the swiftness of a can- 
non-ball) it would reach the orbit of Mercury in 
8 years 276 days; of Venus in 16 years 136 days; 
of the earth in 22 years 226 days ; of Mars in 34 
years 165 days; of Jupiter in 1 17 years 237 days; 
and of Saturn in 215 years 287 days. 

E. Amazing to think that a cannon-ball would 
be upwards of 200 years in going from the sun to 
the remotest planet of the system ! The distance 
must indeed be immense ! 

N. Great as you think it (and to be sure great 
it is,) yet some of the comets go almost fourteen 
times as far from the sun as Saturn is: notwith- 
standing which, they are then nearer to the sun 
than to any of the stars. For if any comet should 
go as near to any star as it is to the sun, when far- 
thest from him, it would be as much attracted by 
that star as it is then by the sun ; and its motion 
being then toward the star, it would go on, and 
become a comet to that star ; and we should never 
hear of it any more.... And now, Euciosia, what do 
you think of the distance of the stars ? 

E. I am lost in wonder ?...,But supposing there 
were no comets, pray is there any other way by 
which we might know that the distance of the 
stars in so inconceivably great ? 

N. I shall only tell you of one way.... If we are 
at a great distance from two neighbouring houses, 
they seem to be small, and at a Utile distance from 



40 

bne another. But as we approach nearer and nearer 
to them, they seem to grow bigger and bigger* 
and the distance between them toencrease. You 
know this. 

is. Very well : please to proceed. 

N* The earth goes round the sun every year, 
in an orbit, which is upwards of 190 millions of 
miles in diameter.. ....Hence, we are 190 millions- 

of miles nearer to some of the stars just now, than 
we were half a yean ago, or shall be half a year 
hence ; and yet, for all that, the same stars still ap- 
pear to us of the same magnitude, and at the same 
distance from each other, not only to the bare eye, 
but also when viewed by the nicest made instru* 
xnents ;... .which shews very plainly, that the whole 

diameter of the earth y s orbit is but a dimensionless 
point in comparison to the distance of the stars. 

E. All further proofs of the immense (and, I 
should think, almost infinite) distance of the stars, 
would be superfluous. But, as we were talking 
about the comets, pray, are they not dangerous ? 
We are always frightened when we hear of their 
appearing, lest their fiery trains should burn the 
world. 

N. That is owing to people's not knowing better. 
The orbits of the planets are all nearly in the same 
plane (as if they were circles drawn on a flat 
board,) but the orbits of the comets are elliptical, 
and all of them so oblique to the orbits of the pla- 
nets, and also to each other, that no comet can ever 
touch a planet. And, as to those appearances^ 



41 

which are called the tails of the comets, they am 
only thin vapours, which arise from the comets 7 . 
and which could not hurt any planet, if it should 
happen to go through that vapour when the comet 
is crossing the plane in which the planet's orbit 
lies. If these trains were fire, we could not see 
any thing through them that is beyond them. For, 
if you hold a candle between you and any object* 
you cannot see that object through the flame cf 
the candle ; but the smallest stars are seen through 
the tail of a comet. 

£• This is comfortable doctrine indeed. 

N. Besides, you know that the world must be 
converted to Christianity before it be burned; 
which, we can hardly believe will be within the 
time that you and I can live, according to the or- 
dinary course of nature. 

E* Alas, brother ! our people who go into those 
remote parts where Christianity was never heard 
of, behave so unjustly and cruelly to the poor na- 
tives, as might rather frighten them from the 
Christian religion, than to induce them to em- 
brace it. I confess I am not at all surprised, when 
I hear, that the native Americans rise sometimes 
in large bodies, and destroy those who call them- 
selves Christians, on account of their barbaious 
ways of using that people. 

iV. It is not at all to be wondered at : for theii? 
principles are, good for goody and evil for evil* 

Jb. As it makes me melancholy to think or speak 
of tuese thing3 $ I beg we may resume our in> 

d & 



42 

tended subject. Considering how far the planets 

are from the sun, and in what times they go round 
him, they must move very fast in their orbits* I 
should be glad to know how many miles they 
move every hour. 

A T . Mercury moves 109,699 English miles every 
hour; Venus, 80,295; the Earth, 68.217; Mars, 
55,287; Jupiter, 29,083 ; and Saturn, 22,101. 

E. And so we are carried 68,217 miles every 
hour, along with the earth in open space, without 
being in the least sensible of that rapid motion. 
N* We are indeed, sister. 

E. And can you tell me what the magnitudes 
of the sun and planets are ? 

N* When the distance of an object is known, 
there are easy geometrical rules for deducing its 

real bulk from its apparent bulk According to 

the fore-mentioned distances, the sun's diameter 
is893,7C0 miles (and consequently he is 1,410,200 
times as big as the earth ;) Mercury's diameter-, 
3100; Venus's, 9360; the Earth's, 7970; Mars's 
diameter, 5150; Jupiter's, 94.100; and Saturn's 
diameter, 77,990 English miles. =* 

The moon's distance from the earth's center is 
240,000 English miles, her diameter is 2170; she, 
moves (with respect to the earth) 2290 miles iiv 
her orbit every hour ; and she goes round the 

* As the distances are now found to be greater thaa 
they were computed to be before the year 1761, die 
diameters must be so much larger in proportion than, 
the former computations made them* 



43 

earth from change to change, in 29 days, 12 hours. 
44 minutes. 

Jupiter has four moons, going round him in 
different times and at different distances. His 
first, or nearest moon, goes round him in 1 day, 
18 hours, 36 minutes ; the second in 3 days, 13 
hours, 15 minutes ; the third in 7 days, 3 hours, 
59 minutes, and the fourth or farthest moon from 
him, in 16 days, 18 hours, 30 minutes. 

Saturn has five moons, the nearest cf which 
goes round him in 1 day, 21 hours, 19 minutes ; 
the second, in 2 days, 17 hours, 40 minutes ; the 
third in 4 days, 12 hours, 25 minutes \ the fourth, 
in 15 days, 22 hours, 41 minutes ; and the fifth, 
or outermost, in 79 days, 7 hours, 48 minutes. 
This planet is encompassed by a broad thin ring ? 
set edge-ways round it, and the distance of the 
ring from the planet is equal to the breadth of the 
ring. The sun shines for almost 15 of our years to- 
gether on the northern side of the ring, then goes 
off, and shines as long on the southern side of it : 
so there is but one day and one night on >each side 
of the ring, in the time of Saturn's whole revolu- 
tion about the sun, which takes up almost 30 of 
our years. 

E. A long day and night indeed, for the inhabit- 
ants of the ring, if any such there be. Undoubt- 
edly, if it is inhabited, it must be by beings very 
different from us ; as we have no reason to believe, 
but that the DEITY has accommodated their 
days and nights as well for them as he has ours 



44 

for us..... But you told me, that the other planets 
turn round their axes, as our earth does : do they 
all turn round the same way, or eastward, so as 
to make the sun and stars appear to go round 
westward; and in what times do they turn round? 
JV* By viewing them with good telescopes, we 
see spots upon most of them, which adhere to 
their surfaces, and appear and disappear regular- 
ly on their opposite sides. By the motions of 
these spots, which are all eastward, we know that 
Venus turns round her axis in 24 days, & hours, 
of our time ; by which divide 225 of our days, the 
time in which Venus goes round the sun, or the 
length of her year ; and we shall find, that her 
year contains only 9^ of her days. Mars turns 
round, in 24 hours, 40 minutes, of our time ; and 
Jupiter in 9 hours, 56 minutes. We cannot tell 
in what times Mercury and Saturn turn round 
their axes, because no stops have been seen upon 
them, even by the best telescopes. The sun turns 
round his axis in 25 days, 6 hours, from West to 
East, also. 

E. Why should the sun turn round ; for as he 
is the fountain of light, he can have no days and 
nights. 

Nm To turn away his dark spots from long 
facing the planets, and thereby to dispense his light 
the more equally all around him to the planets. 
But, are you not tired by this morning's long con* 
versation I 



1 ; s> 

£. Far from it, brother, though I am sure you 
may. But what shall I do ? for I fear I cannot 
remember much of what you have told me this 
morning, so as to write it down. 

JV. Never mind that, Eudosia j for I believe I 
shall publish these our conversations, for the sake 
of other young ladies : many of whom are, no 
doubt, willing to learn Astronomy, but have no 
body to teach them. And then you can have the 
whole together in print. 

£• If you do, sir, I must insist upon your not 
mentioning my name.* 

N. Your desire shall be complied with. 

• Several years ago, I had the pleasure of instruct* 
ing a young lady, who, for goodness of heart, acuteness 
of judgment, and strong inclinations to learn astrono- 
my, answered exactly to the account here given of Eu- 
dosia. 



46 



DIALOGUE III, 



ON GRAVITY AND LIGHT, 



Neander. SO, sister, I. find you are not willing 
to slip the morning opportunity, when we can be 
undisturbed, and by ourselves. Have you made 
any remarks upon our last conversation ? 

Eudosia. Yes, brother. In the first place, I 
remember you told me, that the planet Mercury 
moves 109,699 miles every hour in its orbit, and 
Saturn only about 22,000. I observed likewise, 
that the further the planets are from the sun, they 
not only take longer times to go round him, but 
also move slower in every part of their respective 
orbits. Can you assign any reason for this i 

M The nearer that any planet is to the sun, the 
more strongly it is attracted by the sun \ the far- 
ther any planet is from the sun, the less is the force 
of the sun's attraction upon. it. And, therefore 
those planets which are the nearer to the sun must 
move the faster in their orbits, in order thereby 
to acquire centrifugal forces equal to the power 
of the sun's attraction : and those which are the 



47 

farther from the sun must move the slower, in 
order that they may not have too great a degree 
of centrifugal force, for the weaker attraction of 
the sun at those distances. 

E* Then I understand, that the sun's attraction, 
at each particular planet, is equal to the centrifu- 
gal force of each planet; and, by that means, the 
planets are all retained in their respective orbits. 
Is it not so? 

iV. Accurately so. 

E. Then, as the power of the Deity is manifest, 
in having set off such large bodies as the planets 
are, with such amazing degrees of velocity ; so 
his great wisdom is conspicuous, in having so ex- 
actly adjusted their velocities, and, consequently, 
their centrifugal forces, to the different degrees of 
the sun's attraction at the distances the planets are 
from him.,.. Here is a wonderful balance indeed! 
Can there be an atheist ? I am sure no man could 
be so, after hearing such things as you have told 
me of. 

A r . 'Tis said there are atheists ; but they must 
all be stupid fools. The Almighty has laid the 
great book of nature open to our view ; so that, 
every one that runs may read. Supposing matter 
had existed from eternity (which, by the bye, is 
too great a compliment to be paid to matter,) I 
imagine the greatest atheist in the world could 
hardly bring himself to believe that stones could 
have hewed thenseh es, bricks made themselves, 
trees shaped themselves into beams and boards, 



48 

and mortar made itself ; and then all these mate^ 
rials have jumbled themselves together, so as to 
build a house. And what is a house in compa- 
rison to a planetary system ; or the skill required 
to build it when compared with the organization 
of any insect ? 

£. Nothing at all. But I am apt to lead you 
into digressions. Doth the power of the sun's 
attraction decrease in proportion as the distance 
from him increases ? 

N. No : his attractive force diminishes in pro- 
portion as the squares of the distances (that is, as 
the distances multiplied by themselves) from him 
increase. So that, at twice the distance from the 
sun's center, his attractive force is four times less; 
at thrice the distance, it is three times three times, 
or nine times less 5 - at four times the distance, the 
attraction is four times four times, or sixteen times 
less ; and so on. And this we find, from the com- 
parative distances of the planets from the sun, and 
their different velocities in their orbits : besides, I 
have often seen this experimentally confirmed by 
a machine called the whirling table* 

JS. Ill understand this ; supposing there are four 
planets so placed, as that the distance of the second 
from the sun is twice as great as the distance of the 
first; the distance of the third, three times as great; 
and the distance of the fourth, four times as great 
as the distance of the first: the fourth will be at- 
tracted only with a sixteenth part of the force 
wherewith the first is attracted ; the third only with 



49 

a ninth part of the force; and the second with only 
a fourth part of the force that attracts the first. 

A 7 . Exactly so. 

£. I should be glad to know the reason why 
the sun's attraction decreases in proportion to the 
squares of the distances from him. Why do you 
shake your head ? 

N. Because you ask me a question which Sir 
Isaac Newton himself could not solve, although 
he was the prince of philosophers. 

E. But can you give me no idea at all of it? 

N. I could ; and a very plain one too, if the at- 
tractive force (the effect of which we call gravity) 
acted only according to the surface of the attract- 
ed body. 

E. Your if implies that it does not : but, if it 
did, why should it decrease in that proportion. 

iV. I have drawn a figure for your inspection 
(PLATE II. Fig. 1.) which indeed is for a quite 
different purpose : but it would exactly solve your 
question, if gravity acted, as all mechanical caus- 
es do, only on the surface of bodies. 

Let S be the center of the sun ; and *£/, Se f Sfi 
Sg, be, as it were, lines of attractive force, drawing 
the three square plates A, /?, and C\ toward S* 
These lines touch only the four corners of the 
plates ; but we may suppose the whole space with- 
in them to be full of such attractive, lines, laying 
hold of all the parts, or points (if you will) of the 
surface of each plate : and every particle of mat- 




■■■•■„:■ ■ I 







ter in each plate requiring an equal degree of 
power to draw it equally fast toward the sun. 

Now, let the plate B be twice as far from the 
sun's center as the plate A is ; the plate C three 
times as far, and the attractive forces equal on each 
plate, as if the above-mentioned four lines Sd, Se t 
Sf f and Sg, were four cords, equally stretched, 
and pulling all the plates with equal forces toward 
SL But, the plate B being twice as long, and twice 
as broad as the plate A, it is plain, by the figure, 
that B contains four times as much surface as A 
does, and four times as great a quantity of matter, 
supposing it as thick as Aj and the plate C, being 
three times as broad and three times as long as A, 
contains nine times as much surface and matter as 
A does, supposing it of an equal thickness with A. 
Suppose now, that the intermediate lines of at- 
traction* between the four corner lines, are so closfe 
together, as that they lay hold of every point of the 
r^irface of -4, and draw it toward S with all their 
ibrce : it is plain, that they can only lay hold of eve* 
ry fourth point of the surface of B y and of every 
ninth point of the surface oft?, so that, the plate 
3 will want three fourth parts of the attraction 
that would be sufficient to draw it toward S as fast 
as the plate A is drawn ; and C will want eight ninth 
parts of the attraction that would be sufficient to 
make it move as fast as A moves toward S. 

E. I see tjjis very well : but, if gravity acts no t 
according to the quantity of surface, pray how 
doth it act ? 



51 

1\ T . Exactly in proportion to the solid contents of 
bodies ; that is, to the quantities of matter they con- 
tain. For, you know, that if you would take the 
plate C as it is, and weigh it in a balance ; then take 
it out, and cut it in tho lines drawn on its furface, 
by which means you would divide it into nine 
square pieces : if you then lay them above one an- 
other in the scale, they will be just as heavy as they 
w r ere before, when they lay at each other's edges, all 
in one piece, in the scale. Or, if you suppose them 
to be so cut, and then joined together at each other's 
backs, and put them at the distance S c from the 
sun, as before : they will have only a ninth part of 
the surface toward the sun as before ; and yet, the 
sun's attractive force on them will be just the same. 

E. Then, it seems, there is no way of accounting 
for the manner in which gravity acts, but by re- 
solving it into the will of the Deity ; seeing that the 
quantity of surface has nothing to do in the case. 

iv> Indeed there is not. And, therefore, when 
I henceforth speak of gravity I would have you 
always understand, that I do not thereby mean a 
cause^ but the effect of a cause, which we do not 
comprehend. Besides, you know, that if gravity 
acted according to the surfaces, or bulks of bo- 
dies, a cork would be as heavy as a piece of lead 
of the same bulk as the cork. 

E. Very true.. J3ut, as you told me that the figure 
we have been looking at, w r as not intended to shew 
how gravity acts ; may I enquire what you intend 
to teach me by it, as you said you drew it for me ? 



*v ~* 



- * It is to shew, that the light of the sun, or of 

y otTiei luminous body decreases in proportion 
as the square of the distance from the luminous 
body increases. The rays of the sun's light go 
out in straight lines from all points of the sun's 
surface : and, consequently, the farther they go off 
from the sun, the more they spread; and so they 
cover the more of the surfaces of bodies at the 
greater distances. 

£. How is it known that light moves in straight 
lines ? 

JV. Because, if we endeavour to look at the 
sun, or at a candle, through the bore of a bended 
pipe, we cannot see it ; but through a straight 
pipe we can. 

-E. Enough, brother; please now to explain the 
figure. 

N. Let S be the sun's center, and S d, S e, Sf, 
S jf, be four ra\ s of light, going out from the sun's - 
surface in straight lines (in the same direction as if 
they proceeded from his center,) and suppose the 
space within these rays to be filled with otheis. 
Take the distances S A, SB, S C\ from the sun's 
center, so as SB shall be twice as great as S A } 
and S C thrice as great. Then, at the distances 
S A place the litde square plate A, on which all the 
ravs will fall that fill the above-mentioned space at 
A. At the distance S B> place th- square plate Z>, 
which being twice as long and twice as broad as 
the plate A, it contains four times as much surface 
as A does : and if A be taken away, all the light 
that fell upon it, will fall upon, and cover the 



5$ 

whole surface of B ; which being four times as 
large in surface as A is, and having only as much 
light upon it as A had, every point of the surface 
of B can have no more than a fourth part of the 
light that fell upon every point of the surface of A* 
And, lastly, at three times the distance S A, place 
the square plate C ; which being three times as long 
and three times as broad as the plate A, it con- 
tains nine times as great a surface ; and then if B 
be taken out of the way, so as to let all the light 
that fell upon it go on to the plate C, the light will 
just cover the surface of that plate \ which being 
nine times as large as the surface of A, and hav- 
ing no more light upon it than A had, 'tis plain^ 
that the light upon every point of C is but a ninth 
part so strong and vivid as it was upon every point 
of A. 

E. Nothing can be plainer than this : and it fol- 
lows of course, that at four times the distance of 
A from the sun, his light is sixteen times weaker 
than at A; at five times the distance, it is twenty- 
five times weaker : and so on. I thank vou for 

* ml 

making this so plain. 

N. Indeed I deserve none of your thanks for it, 
I copied the figure from Doctor Smith's Optics, 
That worthy genueman was my good old master ; 
and he is master of Trinity College in Cambridge,, 

jB. Seeing that the comparative distances of all 
the planets from the sun are known, I make no 
dSubt but you can tell me, what the comparative 
quantities of the sun's light on all the planets are* 

£ 2 



54 

N. Ver easily... •The sun's light is seven times 
as great on Mercury as on the Earth ; about twice 
as great at Venus ; at Mars, it is not half so great,, 
or strong, as we have it on the Earth ; at Jupiter* 
only a twenty-eighth part so strong as at the Earth ; 
and at Saturn, is but about a ninetieth part so 
strong as with us. 

E. Then, I should be almost tempted to think,, 
....but I cannot.. ..will not indulge such a thought,, 
as that the Deity is partial : for I cannot imagine 
the inhabitants of our Earth to be better than those 
of the other planets. On the contrary, I would 
fain hope they have not acted so absurdly with re- 
spect to him, as we have done. 

N* Tell me freely what the thought was that 
arose in your mind, which you are so willing to 
suppress.. ..The Deity is no other way a respecter 
of persons than that of properly distinguishing be- 
tween the good and the bad ; and so rewarding the 
one, and punishing the other accordingly. 

E. It seemed to me, that the inhabitants of the 
nearest planets to the sun must be blinded by too^ 
much light; and that those of the farthest planets 
from the sun must be punished all their lives, with 
so weak a light, as can be called little better than 
darkness..... We could not bear seven times as 
much light as we have from the sun ; nor be able 
to do our work w 7 ith only a ninetieth part of the 
light we have. 

JV. Your reflection, sister, is very natural. But,. 
after asking you two or three plain questions, I 



55 



believe I shall be able to give you full satisfaction 
on that head. 

E. Pray ask them, and I will answer them if I 

pan. . . 

N. After you have been a while out m the 
snowy street, can you see as well to work with 
your needle immediately on coming into your 
room, as you did before you went out. 

E. No. 

N. Can you bear the strong reflection of the 
sun's light "from the snow, just as well when you 
go. out into the street, as when you have been 
walking half an hour in it I 

E. No. 

N. Can you give such a reason ior this as would 
satisfy a philosopher ? For you know that the snow 
reflects not less light for your having been a while 
walking in it ; nor is your room a bit the darker 
for your having been out of it. 

E. I wish I could, but indeed I cannot. 
N.. Then I will tell you... .Our eyes are made 
so, that their pupils (which let in the light, where- 
by we see objects) dilate when the light is weak r 
that they may take in the more of it ; and contract 
when the light is strong, that they may admit the 
fewer of its rays. Whilst you are in your room r 
the pupils of your eyes are dilated ; and for that 
reason, when you go out, they take in too much 
of the light reflected from the snow, which you 
find is hurtful. But they soon contract so, as to 
admit no more of that strong light than you cars 



56 



easily bear. And then, when you come into your 
room, with the pupils of your eyes contracted the 
room, being not so light as the street, appears 
darker to you than it did before you went out : 
but, in a short time, the pupils dilate again ; and 
then they let ,n a sufficient quantity of light for you 
to work by. J 

No, v , supposing all the other planets to be inha- 
bited by such beings as we are (though, for rea- 
sons I shall pfctitton afterwards, we cannot believe 
hey are,) ,f the pupils of their eyes who live on 
the pianet Mercury are seven times as small as 
ours are the light will appear no stronger to them 
than it doth to us here. And if the pupils of their 
eyes who live in Saturn are ninety times as larjre 
as ours (wmch they will be, if they are nine times 
and an halt as large in diameter as ours ; and which 
will appear to be no deformity where all are alike, 
and other sorts have never been seen,) th- light 
there will be of the same strength as it is to our 
eyes here ...Pray, Eudosia, how many full mo on S> 
co you think, would there need to' be placed in 
a clear sky, to afford us moon-light equal to 
common day-Kght, when the sun doth not shine 
out, and all our light is by reflection from the 
clouds ? 



£. Indeed I cannot tell :....but am apt to think, 
that sixty, or an hundred, at most, would do. 
For when the full moon is not clouded, she shines 
so clear, that I can read by her light. 



sr 



A r . Sixty, or an hundred !..*»! assure you, that 
you are greatly mistaken : for it would require 
ninety thousand ; and that number would fill the 
whole of our visible sky. 

E. You amaze me ! but I know you will not de- 
ceive me. Pray, how can you find any method of 
comparing moon light with day-light, so as to as- 
certain the great difference between the quantities 

thereof? 

N. Have you never observed the moon pretty 
high up in the morning, after the sun was risen, 
when the moon was about three quarters old ? 

E. Yes, brother : and when I have seen her, as 
it were, among whitish clouds, she appeared much 
of the same colour as they did ; very dim in com- 
parison with what she appears in the night. 

N. And yet, she was just as bright then as she 
is in the night : only the superior light of the day- 
made her seem so much otherwise. Like a can- 
dle, which appears very bright in the night time ; 
but set it in the street in day -light, and it will seem 
very dim, although its real brightness is still the 



same. 



E. I think I could almost tell what you are to 
infer from all this : but will not speak, lest I should 
be mistaken again. And therefore I beg you 

will proceed. 

A r . When the sun is hid by clouds, all the light 
we have is by reflection from them. -The moon 
reflects the sun's light in the night time, as -the 
clouds do in the day ; and as she can reflect no 



58 



more light in the day than a small bit of a whitish 
cloud does that covers as much of the sky as the 
moon, covers ; she can reflect no more in the night. 
And as the full moon fills only a ninety-thousandth 
part of the sky, her light is io more than equal 
to a ninety-thousandth part of common day-light. 
Now, as the light of the sun at Saturn is equal to 
a ninetieth part of his light at the earth, and com- 
mon day-light at the earth is 90,000 times as 
great as moon-light; divide 90,000 by 90, and the 
quotient will be 1000 ; which shews, that the sun's 
light at Saturn is 1000 times as great as the light 
of the full moon is to us. 

£. I see plainly that it must be so Oh ! 

Jvt Why do you sigh, Eudosia P 
£. Because there is not an university for ladies 
as well as for gentlemen. Why, Ntander, should 
our sex be kept in total ignorance of any science 
which would make us much better than we are,' 
as it would make us wiser ? 

N. You are far from being singular in this re- 
spect I have the pleasure of being acquainted with 
many ladies who think as you do. But if fathers 
would do justice to their daughters, brothers to 
their sisters, and husbands to their wives, there 
would be no occasion for an university for the 
ladies; because, if those could not instruct these 
themselves, they might find others who could. 
And the consequence would be, that the ladies 
would have a rational way of spending their time at 
home, and would have no taste for the too com- 



3 



mon and expensive ways of murdering it, by go- 
ing abroad to card-tables, balls ana 1 plays ; and 
then, how much better wives, mothers, and mis- 
tresses they would be, is obvious to the common 

sense of mankind The misfortune is, there are 

but few men who know these things : and where 
that is the case, they think the ludies have no busi- 
ness with them ; and very absurdly imagine, be- 
cause they know nothing of science themselves, 
that it is beyond the reach of women's capacities. 

E. But, is there no danger of our sex's becoming 
too vain and proud, if they understood these things 
as well as you do ? 

N. I am surprised to hear you talk so oddly.. „. 
Have you forgot what you told me two days ago? 
namely, that if you had been proud before, the 
knowledge of Astronomy, you believed, would 
make you humble ? 

E. You have caught me napping, as the saying 
is:. ...but I will not take up more of your time at 
present with digressions. I remember, this morn- 
ing, to have heard you mention the light's going 
from one place to another, as if it took some time 
in moving through open space. I know that sound 
does so ; because I have seen the flash of a dis- 
tant cannon before I heard the noise that it made. 

N. True, sister ; and you did not see the flash 
at the very instant when it was given ; though you 
saw it verv soon after* 

-E. And do you know with what degree of 
swiftness light moves ? 



to 

lv. Yes; and you shall socn know too. The| 
Earth's orbit lies far within the orbit of Jupiter, 

E. Undoubtedly : because Jupiter is much far-] 
ther from the Sun than the t arth is. 

iV. Then you know, that when the Earth is be- 
tween Jupiter and the Sun, the Sun and Jupiter 
appear opposite to each other in the heavens. 
And when the Sun is nearly between us and Ju- 
piter, the Sun and Jupiter appear nearly in the 
same part of the heavens, 
E. Undoubtedly- thev must. 
N, And therefore, when the Sun and Jupiter 
appear almost close together, the Earth is almost 
the whols diameter of its orbit farther from Jupi- 
ter, than vrhen it and Jupiter appear opposite to 
each other in the heavens. 
E. Certainly. 

N. The times when Jupiter's moons must be 
eclipsed in his shadow are easily calculated ; be- 
cause, by telescopic observations, the times in 
which they go round him are accurately known : 
and the apparent vanishing of these moons in the 
shadow may be very well perceived through a 
telescope ; or the instant when they recover their 
light again by the sun's shining upon them, at 
their going out of the shadow. And it has been 
always observed, since telescopes were invented, 
that these eclipses are seen sixteen minutes sooner 
when the E irth is nearest to Jupittr, than when 
it is farthest from him. So that, if there were 
two earths moving round the sun in the same 



6i 

orbit, and always keeping opposite to each other i 
when one of them is at its least distance from Ju- 
piter, and the other at its greatest, an observer on 
the nearest would see the same eclipse sixteen 
minutes sooner than an observer on the farthest 
would: which shews, that light takes sixteen 
minutes to move thro' a space equal to the width 
or diameter of the earth's orbit, which is one 
hundred and ninety millions of miles. And, con- 
sequently, it must take eight minutes of time in 
coming from the sun to the earth ; as the sun is 
nearly in the center of the earth's orbit : that is, 
at the half of one hundred and ninety millions of 
miles, or ninety-five millions of miles from the 
earth* * 

E. I understand this, but a difficulty rises in my 
mind. 

N. Only mention it, and I will remove it if I can. 
E. The rays of the sun's light come directly 
from him to the Earth; but his rays from Jupi- 
ter's moons come to us only by reflection. Are 
you sure that reflected light moves with the same 
Velocity that direct light does ? 

N. There is no reason to believe but that it 
does. And I imagine I can very easily convince 
vou that it does so. 

If the particles of light did not fly off from the 
planets as fast as they came upon them, there would 
still be an accumulation of light upon them ; which 
would make them appear every night brighter and 
brighter j but, in reality, they do not. And if the 

9 



63 

/at flew off faster from the planets than it come* 
on them, they would appear dimmer and dim- 
rner every night ; which is not at all the case. 

E. But are all the rays which the sun darts on 
aiiy planet refected from it, and none of them lost 
or absorbed in the matter of which the planet is 
composed? Or if some of them be absorbed, will 
not this invalidate your argument ? 

Nm Not at all, if the absorbed rays bear a con- 
stant proportion to the whole number of rays with 
v/hich the planet is successively illuminated ; and 
this must undoubtedly be the case ; for the same 
parts of the planet's surface which either reflect, 
or absorb the ravs that fall upon them this moment, 
will be equally disposed to reflect or absorb the 
ravs that fall upon them in the next : and so the 
ie proportion between the absorbed and reflect- 
ed ravs, or between them and the whole quantity 
light thrown on the planet, will be continually 
preserved. % 

E. But what if some parts of the planet's sur- 
face be more hardened by drought, or softened by 
■wet, as on our earth ; or be in any other respect 
more disposed, either to reflect, or absorb the 
Sun's ravs at some times than at others ; would 
not this vary the proportion you have mentioned ? 
X If we may judge of this from our own globe, 
-*.vhere the contrary qualities of drought and wet, 
hardness and softness, smoothness and roughness 
of some parts of its surface, so far as they result 
from any alterations of weather, &c. if taken upon 



9% 

an average far a whole year, or other given time, 
and throughout any half of the Earth's surface ; 
they will, very nearly, if not exactly, balance each 
other. 

The same may be therefore supposed to holcf 
good in the other planetary worlds ; and so the 
proportion before-mentioned will not be sensibly 
altered. 

E. You have quite removed my difficulty, bro- 
ther ; and I thank you for having done it. But, 
as light comes from the Sun to the Earth in eight 
minutes of time, its swiftness must be amazingly 
great. Let me try whether I can compute it : for 
you taught me not only the four common rules o? 
arithmetic before you went to the university, but 
even the rule of three. The Sun's distance from 
the earth is 95 millions cf miles, in round num- 
bers ; and light moves through that space in 8 
minutes of time ; divide therefore 95,000,000 by 
8, and the quotient is 11,875,000, for the number 
of miles that light moves in a minute. Now, I 
remember that you told me, a cannon-ball moves 
at the rate of 480 miles in an hour, which is 8 
miles in a minute ; I therefore divide 11,875,000, 
by 8, and the quotient is 1,484,375 ; so that light 
moves more than a million of times as swift as, at 
cannon-ball. Amazing indeed f 

N. It is so : And now I will tell you something 
which is full as amazing. 

E. What can that be ? Do you mean the power 
of the Almighty ? 



t>4 

. 

-?/. Far from it : I only mean the inconceivable 
rmallness of the particles of light. 

J?. And how do you know that they are so in- 
conceivably small ? 

aV. The force with which a body strikes an 
obstacle, is directly in proportion to the quantity 
of matter in the body, multiplied by the velocity 
with which it moves. And, consequently, as the 
velocity of light is, in round numbers, a million of 
times as great as the velocity of a cannon bullet; 
if a million of the particles of light were but as big 
as a common grain of sand, we could no more 
keep our eyes open to bear the impulse of light, 
than we could to have sand shot point blank against 
them from a great cannon. 

Another way of proving that the particles of 
light are so small as to exceed all human compre- 
hension, is this: Let a lighted candle be set on 
the top of a spire steeple in the night-time, and 
'here will be a very large spherical space filled with 
the light of the candle before a grain of the tallow 
be consumed; and as that grain of tallow is di=- 
vided into so many particles as fill all the space in 
which the light is diffused, can you possibly ima- 
gine how small the particles are into which it is 
so divided ? 

E. Indeed I can form no idea thereof. 

N. A very good computist has found, that the 
particles of blood of those animals which can only 
be seen by means of a microscope, are as much 
smaller than a globe, whose diameter is only a 



; 

XT 



65 

tenth part of an inch, as the small globe is less 
than the whole earth. And yet, that their parti- 
cles of blood are like mountains to a grain of sand, 
when compared with the particles of light. 

E. I am glad to hear our breakfast-bell : for, if 
I should hear more of these subjects at present, I 
know not but that I should for some time, lose the 
power of thinking. 

JV. I had just done with the subject of light 1 ? 
but am sorry to hear that you must go from home 
for a few days on a visit. However, during your 
absence, I intend to draw out two or three figures, 
in order to describe the late transit of Venus to 
you by them : and give you some idea of the me- 
thod by which the distances of the planets from 
the sun were found, by observations made on that 
transit. 

JS. I am very much obliged to you, sir, for the 
trouble you have taken, and are to take further, 
on my account : and shall return as soon as possi- 
ble. You know I could not refuse Miss Good-* 
all's invitation* 



J % 



66 



DIALOGUE IV. 

fN THE TRANSIT OF VENUS, JUNE 6, 1761 ; AND 
ItOW THE DISTANCES OF THE PLANETS FROjfc 
THE SUN WERE FOUND THEREBY. 



Neander. DEAR sister, I am very glad to see 
you again : I suppose you found Mr. and Mrs. 
Goodall, and their daughters, to be very agreeable 
company. 

Eudosia. Quite so, and I have spent three days 
very happily with them. 

N. It was very obliging in Mr. Goodall and 
Miss Sophy to see you safe home. 

E. They would do it, for all that I could say : 
even though I told them, that the servant who 
was sent for me was very careful, 

JV. Mr. Goodall and I spent an hour together 
last night : and though he was full of his praises 
of your good sense, he did nCt say one word about 
our astronomical conversations ; by which, I ima- 
gine, you spoke nothing about them in that family. 
Yet I am far from doubting, that it would have 
feeen very agreeable if you had* 




ntZJtl ^ 




v~ w^ 



FcTiJltSOi' tltl* 



■ ■ 

V Teddfc. 



67 

JE. Truly, brother, if I had, you must have 
heard of it : and then I should not have wondered 
if you had said that I am not over-stocked with 
good sense. I must know these things better be- 
fore I begin to speak of them ; and even then, not 
to speak, unless I am desired by those to whom I 
think the subject will be entertaining. You told 
me, the morning I went away, that our next con- 
versation should be on the transit of Venus ; and 
how the distances of the planets from the Sun 
were found thereby. 

j\ 7 . And to shew you that I have not forgot my 
promise, here are the figures which I told you I 
would draw out for that purpose. (See PLATE 
II. Fig. 2. and '3. and PLATE III. Fig. 1.) 
But in these delineations, we must often sacrifice 
one truth to explain another ; and in the present 
case it is unavoidable. For if we w r ere to make 
the bulks of the planets in our figure no greater 
than they are in proportion to their distances 
from the Sun, the planets would be mere points : 
and a large sheet of paper would be too small for 
the lengths of the lines of distances. So that, in 
order to make the present subject plain, we must 
enlarge the planets, and contract their distances 
from the Sun ; otherwise we could not, at present, 
render the effects intelligible which arise from 
some of the planetary motions. 

£* Very well, brother : please to proceed. 

jV". The diameter of the Earth is no more than 
& point in comparison of its distance from the Sun; 



68 

and therefore, if the Sun were viewed, at the same 
instant, by two observers on opposite sides of 
the Earth, his center would appear to both of 
them to be in the same point of the heavens* 
But, when Venus is between the Earth and the Sun 
(as she was at the time of her late transit,, her 
distance from the Earth is between three and 
four times less than the Sun's distance from the 
Earth. And therefore, if Venus be then viewed by- 
two observers on the Earth, who are at a great 
distance from one another, she will appear to each 
of them, at the same instant, to be on different 
part's of the Sun's surface. ....Thus in Fig. 2. of 
PLATE II. let S be the Sun, V Venus, and 
ABDE the Earth. Let one observer beat A y 
another at Z?, and a third at D ; all looking at 
Venus at the same moment of absolute time. To 
the observer at A, Femis ( V) will appear upon 
the Sun at F: as she is seen in the right line A V F: 
to the observer at jB, she will appear upon the 
Sun at G, being seen by him in the right line B VG: 
and to the observer at -D, Venus will appear upon 
the Sun at iZ, because he sees the planet in the 
right line D V H. Or, if you will suppose Venus 
to be at rest at V y during the time that the ob- 
server at A is carried, by the Earth's motion on 
its axis, from A to Z), through the arc A B D ; 
it is plain, that, to this observer, the planet V will 
appear to be moved on the Sun from F ta If 9 
through the space F G H* 



69 

Let us now suppose, that the Earth aide (Fig, 
S.J is nearer the Sun s than as represented in Fig0 
2. in which case, Venus v will be proportionally 
nearer the Earth; and the arc a bd, through which 
the observer is carried, will bear a greater pro- 
portion to the distance of Venus v from the Earth, 
in Fig. 3, than the same arc A B D (in Fig. 2.) 
bears to the distance of Venus V irova the Earth. 
So that, if one observer should be placed at a, 
another at £, and a third at c, the observer at a, 
would see Venus on the Sun aty, the observer at 
£, would see her on the Sun at^, and the observ- 
er at d % would see her on the Sun at h, all at the 
same instant of time. Or, if Venus kept at rest 
at £, whilst the observer at a was carried from a 
to dby the Earth's motion; Venus would in that 
time, appear to him to have moved from f to h on 
the Sun, But the space f g A, in Fig. 3. is longer 
than the space F G H in Fig. 2. and therefore, 
•the nearer the Earth is to the Sun, the greater 
will the space be through which Venus appears to 
jnove upon the Sun, by the observer's real motion 
along with the Earth, in any given time : and the 
farther the Earth is from the Sun, the less will 
the space be through which Venus appears to 
move upon the Sun, by the observer's real motion, 
in the same time. 

And, consequently, as Venus is really moving 
on in her orbit, in the direction of TV W (in Fig. 
£•), or t v w (in Fig. 3.) whilst the observer is 
carried by the Earth's, motion on its axis from -4 



to D, or from a to J; it is plain, that Venus Will 
appear to move sooner over the sun, if the Earth's 
distance from the Sun be onlj I ; s (as in Fig'. 3.) 
thsn if it be B V S (as in Fig. 2.) So the whole 

ration of her transit over the Sun must be 

:rter, if the Earth's distance from the Sun be 
only b v /, than if it cater, as B To.. ..Do 

rou understand this, Eudoaia ? 

Em I think so plain, that any body might 

understand 

A 7 . Then wc have done wLh these figures, and 

shall proceed . 1. of PLATE III. in which, 

abedebe the Earth, V Venus, and S the Sun. 

T::e Earth ard on its axis, in the di- 

v\abcd; aud Venus moves in her orbit in 

die din E V e. 

jppose th rth to be transparent like 

gb. j at his : 

and kept looking at the Sun S, during aae in 

which Venus c in her orbit from F to /, 

through the spa in this c the 

t n on its axis could have no effect 

on your position, because it could not carry you 
any way from C. Then, when Venus was at F 
in her or old appear to you as at K, just 

within th Sun's surface, touching his eastern edge 
at K ; that is, at htr first internal contact with the 
Sun's eastern edge. As she moves on, from F 'to 
f in her orbit, she would appear to you to move 
on the S in, from Kto Lyin the line KkLy which 
is called the line ef her transit over the &wu And 



when she was %\f in her orbit, she would appear 
at L on the Sun, just beginning to leave his western 
edge, or at her last internal contact with the Sun. 
Now, please to remember, that if Venus could be 
seen from the Earth's center C, she would move 
from F tojfin her orbit, in the time that she would 
appear to move from K to L on the Sun ; or from 
her first internal contact to the last. 

E* A bare inspection of the figure shews it ; 
for, when Venus is at F in her orbit, she would 
appear just within the Sun at R; because then, as 
viewed from the Earth's center C\ she would be 
seen in the straight line C F K; and when she 
came to/" in her orbit, she would seem just be* 
ginning to leave the Sun at i, because she would 
be seen in the straight line C J L* 

A 7 . Very well*... Now let us suppose, that an ob- 
server is placed on the Earth's surface at a; and 
that he is carried from a to b> by the Earth's 
motion on its axis, in the time that Venus moves 
in her orbit from F toJ\ 

When Venus is at F, she appears at K on the 
Sun, as seen from the Earth's center C ; but to 
the observer at a ; she will not appear to be then 
entered upon the Sun ; because (if she were then 
visible in the sky) she would be seen in the line 
A F Hy eastward from the Sun ; and must move 
on from F to G in her orbit, before the observer 
at a can see her on the sun at K^ in the right 
line a G K. So that her transit will begin as 
much later to the observer at a, than it does to 



E observer at C y as she is moving frc.r. Jf :: 
in her orbit. 

When Vcb (bes to g in her orbit, the ob- 

server will be carried he Earth's motion al- 

most from a b ; and then he will s?e 
line c f X. just beginning tc leave the S 
but she must move ; m g : it, be- 

fore she begins to leave the San a: L, a: 3c 
from the Earths ceil . in the right Cor I 

line CfL; and then to the observer at b % she v 

r quite clear of I :n to the West, in the 

line B f L So that th .ole duration of the 

transit from A' to L on the Sun, will be shorter, 
as seen by the observer in motion from a 
than as seen by the (supposed) observer at rest 

Eanh's center C For, to the former, she 
will move only from G to g- in her orbit, cl 
the time she appears to move from Klo L on the 
Sun : whereas, to the latter, she must move from 
F to J in her orbit, in the time shea; 
Sun from A" to i. 

The n e Earth is to the S great- 

er -Tt-rence of the durations of the tran- 

sit A' to L on the Sun, from the 

Ea ce and from its center: and : 

h is from the S 

etween the durations of the tran* 
n from the earth's surface and from 
its center, accordingly. 

M Certainly so, by what y .ready told me 
your explanation of the second and I 



73 

the second Plate. For, the nearer the Earth is to 
the sun, the nearer also in proportion it must be 
to Venus ; and the farther it is from the Sun, the 
farther also it must be from Venus. So that the 
space through which the observer is carried bv 
the Earth's motion from a to b (PLATE III, 
Fig. 1,) will bear a greater proportion to the dis- 
tance of Venus from the earth in the former case 
than in the latter : and so, will affect the times of 
durations of the transit, as seen from the Earth's 
center, and from its surface, accordingly. .•.But I 
should be glad to know, why you suppose an ob- 
server to be placed at the Earth's center, as it is a 
thing impossible to be done; and if he was there, 
he could neither see the Sun nor Venus. 

N. Because the motions of the planets are cal- 
culated in the astronomical tables, as if seen by an 
observer at rest. And as the apparent breadth of 
the Sun is known, and the time of Venus's going 
round the Sun is also known ; the time of her ap- 
pearing to move through a space equal to the 
Sun's breadth, as seen by an observer at rest, is 
easily calculated, and is the same as w r ould be ob- 
served by a person placed at rest at the center of 
the Earth. And then, at all kinds of distance 
of the Earth from the Sun, it is easier to calculate 
how much the duration of the transit w r ould be 
shortened bv the motion of an observer on the 
Earth's surface, on the side of the Earth next to 
Venus, and who is then moving in a contrary di- 
rection to the motion of Venus in her orbit, than 

G 



n 

the duration of the transit would be to an observ- 
er at the Earth's center, or even on its surface if 
the Earth had no motion on its axis ; in which case, 
the observer on the surface would be at rest. But 
as that observer is really in motion with the Earth, 
when the duration of the transit is observed by 
him, and consequently, known how much short- 
er it appeared to him, than it would have done if 
he had been at rest ; the distance of the Earth from 
the Sun may thereby be found : which, as I told vou 
already, is thereupon computed to be 95,173,000 
English miles. 

E* The distance of the Earth from the Sun, in 
hiiles, being known, I should be glad to know how 

: find the distances of all the other planets from 
the Sun. For we cannot send people from the 

arth to those planets, to observe transits. 

N. I told you already, in our second dialogue, 
that the relative or comparative distances of all 
the planets from the sun are known long ago 3 both 
by the stated laws of nature, and by observation ; 
and that thev are as follows. 

If we suppose the Earth's distance from the 
Sun to be divided into 100,000 equal parts (let 
these parts contain how many miles they will.) 
Mercury's distance from the Sun must be equal 
to 58, riO of these parts: Venus's distance, 72, 333; 
Mars's distance, 152,369 ; Jupiter's, 520,096 ; and 
Saturn's distance, 954,006. 

Now, as the number of miles is in proportion 
to the number of parts, and the 100,000 parts by 



75 

Which the Earth is distant from the Sun, contains 
95,173,000 miles ; we say, by the rule of three, as 
100,000 parts are to 95,173,000 miles; so are 
38,710, Mercury's distance from the Sun in parts, 
to 36,841,468, his distance from the Sun in miles. 
So are 72,333, Venus's distance from the Sun in 
parts, to 68,891,486, her distance from the Sun in 
miles. So likewise are 152,369, Mars's distance 
from the Sun in parts, to 145,014,148, his dis- 
tance from the Sun in miles. And so are 520,096, 
Jupiter's distance from the Sun in parts, to 
494,990,976, his distance from the Sun in miles. 
And, lastly, (carrying on proportions,) so ar£ 
954,006, Saturn's distance from the Sun in parts? 
to 907,956,130, his distance from the Sun in 
miles. 

E. I thank you, brother, for having explained 
the whole of this matter so much to my satisfac- 
tion. But I have heard that the late transit was 
observed by people at very different parts cf the 
Earth. Pray did you find, that ail the observa- 
tions (as you got accounts of them) agreed so 
well, as to give all the same conclusion ? 

N. I cannot say they did, so nearly as we could 
wish ; which might have been owing to two caus- 
es. First, that the differences of longitude (as it 
is called) between many places* where those ob • 
servations were made, are not yet well ascer- 
tained : and secondly, that all the observers did 
not use telescopes, of an equal magnifying power 
which they should have agreed to do before-hand > 



>• 



6 



And undoubtedly, they who used the highest 
magnifying telescopes, could more accurately de- 
termine the instants of Venus's two internal con-> \ 
tacts with the sun, than those could who used 
smaller magnifying telescopes. But it is to be 
hoped, that all proper care will be taken, in ob- 
serving the transit on the 3d of June, 1769. And 
astronomers will do well to make the most and 
best of ft they can ; as there will not be another 
transit in less than 105 years afterward. 

£. How can thctt be?. ...For as the Earth goes 
round the Sun in a year, and Venus in 225 days ; 
I should think, that Venus would pass between 
the Earth and the Sun once every two years at 
most. 

N- So she would, once in ever} 7 584 days, if her 
orbit lay in the same plane with the Earth's or- 
bit, like one circle made within another on a flat 
paper. But one half of Venus's orbit lies on the 
North side of the plane of the Earth's orbit; and 
the other half on the South side of it : so that her 
orbit only crosses the Earth's orbit in two oppo- 
site points. And therefore, Venus can only pass 
directly between the Earth and the Sun, when, at 
the times of her conjunctions with the Sun, she is 
either in or near one or other of those points. 
At all other times, she either passes above or be- 
low the Sun, and is then invisible, on account of 
her dark side being toward the Earth. But its 
being so also, at the time of her late transit, made 
her very conspicuous on the Sun, like a black 



77 

patch on a circular piece of white paper. At her 
last transit, she passed below the Sun's center, 
about a third part of the Sun's breadth ; and at 
her next, she will pass as far above it. 

E. I understand this thoroughly,. ..But, I think, 
there are some lines in the figure (PLATE III. 
Fig. 1.) which you have not yet explained. 

N. Then shew me them, and I will. 

J?. They are the lines NEK and n e Z. 

N* True : I had almost forgot them. Suppose 
an observer at JV, on the side of the Earth farthest 
from Venus, to be carried from Nto n in the same 
direction with Venus's motion in her orbit from 
E to e, in the same time that au observer at a is 
carried from a to h, in a contrary direction to the 
motion of Venus in her orbit : the duration of the 
transit will be longer, as seen by the observer who 
is carried from iVto ?z, than it would be to an ob- 
server at rest at the Earth's center C7. For, when 
Venus is in her orbit at jB, she will appear upon 
the Sun at K y as seen frem N in the right line N 
E K; but she must go on from E to F before she 
can be seen from 67, upon the Sun, in the right 
line C F K: and, as seen from C\ in the right line 
C f L, she will appear as just beginning to leave 
the Sun at i, when she is at f in her orbit. But 
she must move on, from f to £, before she can ap- 
pear as beginning to leave the Sun, when seen by 
the observer at w, who is carried from N to n by 
the Earth's motion on its axis, in the time of Ve- 
nus's moving from £ to e in her orbit. So that 

G 2 



T8 

the visible duration of the transit will be longer 
as seen by an observer who is carried from N to 
;z, than it would be to an observer at rest ; and 
shorter, as seen by an observer who is carried 
from a to b* And the difference between these 
visible durations will be of greater advantage to- 
wards finding the Earth's distance from the Sun, 
than what could be gained only from observations 
made on the side of the Earth w T hich is nearest to 
Venus, during the time of her transit. 

E. Pray, who was it that first thought of this 
method of finding the distances of the planets from 
the Sun? I imagine he must have been a very 
great astronomer. 

-A 7 . He was so indeed: the man who first pro* 
posed this method was the great Doctor Hai^leY* 
And as he was morally certain, that, according ta 
the common course of nature, he could not live 
to see that transit, he most earnestly recommend- 
ed it to future astronomers, that they might ob- 
serve it when he was dead. And, in order to fur- 
nish them with all proper information, he gave in 
a paper on the subject to the Royal Society; 
which paper was, soon after, published in the 
Philosophical Transactions* 



T9 



DIALOGUE V- 



ON THE METHOD OF FINDING THE LATITUDES, 
AND LONGITUDES OF PLACES. 



:o: 



Neander. GOOD-MORROW, sister: you? 

have been later than usual of coming this morn- 
ing What is the matter ? You look pale. 

Eudosia. I was taken ill last night about twelve, 
of an ;t.stjima, which frightened me, as I was nev- 
er so before ; and kept me awake till five o'clock 
this morning. Then it left me, and I fell asleep, 
and have quite over-sleeped my time ; for now it 
is eight o'clock. 

N. Why did you not ring your bell, in order 
that something might have been brought to re- 
lieve you? especially as you know that our mo- 
ther (among many other good medicines) always 
keeps an electuary of honey, powder of liquorice r 



80 

of elecampane, seeds of anise, and flowers of sul- 
phur ; which is exceeding good for that disorder, 
and has cured many of it. 

E. I was loth to surprise any body in the night, 
especially as the asthma did not continue long 
violent. ..I raised my head a good deal ; so it left 
me gradually ; and now I feel nothing of it. 

JV. I am very glad of that.. ..But I think it would 
be quite wrong to enter upon any such subject this 
morning, as we have already been about. And 
therefore, I hope you do not come now with any 
such intention. 

En Indeed I do, if it were but to take oft my 
drowsiness ; and I feel no other ailment at pre* 
sent. 

A r . Well then, with what subject shall I enter- 
tain you this morning? 

E. I heard you yesterday, for the first time, 
mention the Longitudes of Places. But as I scarce 
know what either Longitude or Latitude means, I 
should be glad to know : especially as we have 
heard so much lately about the finding the Lon- 
gitude. And as I never heard of any difficulty 
about finding the Latitude, I imagine, the latter 
is much more easily found than the former. 

N. It is so indeed, sister. 

E. What is the reason of that ?.. ..But I believe 
mv question is premature : for I should have asked 
first, what those terms mean : 

N. Right, Luuosia ; and now I will inform 
vou....-Ev'eri/ circle, be it great or small, is divided 



81 

(or supposed to be divided) into 360 equal parts, 
called Degrees. Now, if we take a great circle 
round the Earth, which divides the Earth into 
two equal parts, every degree of that circle con- 
tains 69^ English miles : as is the case with the 
degrees of the equator, and nearly so with those 
of a great circle taken round the Earth, through 
the North and the South poles. 

The Latitude of a place is the number of de- 
grees that the place is from the Equator, towards 
the North or South pole: and is denominated 
North or South, as the given place is on the North 
or South side of the Equator.. •.Thus, in the little 
globe {Fig. 1. of PLATE I.), all the places in 
the northern hemisphere, from every point of 
the equator to the North pole, have North 
Latitude : and all the places from every point of 
the equator to the South pole, have South Lati- 
tude. As the poles are the farthest points of the 
Earth from the equator, they have the greatest 
Lat'tude ; which is 90 degrees, or a fourth part 
of 360. the whole circumference of the globe. 

The North and South points, or poles of the 
Heaven, are directly over the North and South 
poles of the Earth. And therefore, as the Earth 
turns round its axis, which terminates in its 
North and South poles, every point of its surface 
is carried round in twenty-four hours, except its 
poles, which are at rest. This motion of the 
Earth will cause an apparent motion of every 
point of the Heaven, in a direction contrary to the 



82 

Earth's motion, excepting its poles, which appear 
always at rest ; because they are directly over the 
poles of the Earth, which are at rest. 

E. May I put in a word just now, before you 
proceed farther ? 

N. Why not? 

E. I should think that the poles of the Heaven 
would change among the stars, on account of the 
Earth's motion round the Sun in a year. For, 
undoubtedly, if the Earth's axis (or line on which it 
turns round every twenty-four hours) were pro- 
duced to the Heaven, it would describe a circle 
theiein, equal in diameter to that of its whole 
orbit ; which you have already told me is 190 
millions of miles. 

N. And so it does. But if it should, by its 
track, make as dark a circle in the Heaven> as 
£an be made with ink by a pair of compasses on 
paper, the distance of the starry Heaven is so great 
from us, that a circle therein of 190 millions of 
miles in diameter, would not appear to us so big 
as the smallest dott you can possibly make with a 
fine pen upon paper. Which shews, that if the 
Earth were as big as would fill its whole orbit, it 
would appear no bigger than a dimensionless point, 
if seen from the stars. For, notwithstanding the 
Earth's constantly changing its place in its orbit, 
the poles of the Heaven could never be perceived 
to change their places, a single visible point, even 
when observed with the nicest instruments. And 
therefore, we always consider the poles of the 



83 

Heaven to be fixed points ; and to keep constantly 
just over the poles of the Earth. 

E. You have satisfied me entirely on this head; 
and at the same time, convinced me, that the dis- 
tance of the stars must be inconceivably great. 
Now, please to proceed. 

N* Let us suppose a great circle to be drawn 
round the Heaven, through its North and South 
poles and to be divided into 360 degrees, like a 
circle drawn round the Earth through its North 
and South poles. 

As the Earth is but a point in comparison to the 
distance of the starry Heaven ,* let us be on what 
part of the earth we will, we see just one half of 
the Heaven, if the horison, or limit of our view 
all around, be not intercepted by hills. And as 
the poles of the Heaven are directly over the poks 
of the Earth; so the equinoctial in the Heaven is 
directly over the Earth's equator, all around. 

Now, as the Earth is round, and the Heaven 
appears to us to be round like the concave 
surface of a great sphere or hollow globe ; it 
is plain, that if we were at the Earth's equator, 
the equinoctial in the Heaven would be over our 
heads, and the North and South points, or poles 
of the Heaven, would appear to be in the North 
and South points of our horizon, or limit of 
view. But if we go one degree from the equa- 
tor, towards either the North or South pole of 
the Earth, the like pole of the Heaven would 
appear to be one degree elevated above our 



84 

horizon, because we would see a degree of the 
Heaven below it ; and the contrary pole of the 
Heaven would be one degree hid below the limit 
of our view. If we go two degrees from the 
equator, the pole will appear to be two degrees 
elevated above our horizon ; and so on, till we go 
to either of the Earth's poles, 90 degrees from the 
equator ; and then, the like poles of the Heaven 
would be just over our head, or 90 degrees above 
our horizon ; which is the greatest elevation it 
can have, as seen from any part of the Earth. 
And as the number of degrees we are from the 
Earth's equator is called our Latitude, so the 
number of degrees of the elevation uf the celestial 
pole is equal thereto. At London, the North 
pole of the Heaven is elevated 51^ degrees above 
the horizon; which shews, that London has 5l£ 
degrees of North Latitude from the equator. 
And as Latitude begins at the equator, the places 
thereon have no Latitude at all. 

E. But how can you tell by what number of de- 
grees the poles is elevated I for there is no visible 
circle in the Heaven divided into degrees, to 
reckon by. 

N. But we have an instrument called a Quadrant* 
which is a quarter of a circle, drawn on a plate of 
metal, and divided into ninety degrees ; and it 
has a plumb line with a weight hanging from its 
center, which line always hangs toward the Earth's 
center, when allowed to hang freely. And if we 

k at the pole along one of the straight edges of 



85 

the quadrant, the other edge will be as many de- 
grees from the plumb line, as are equal to the 
number of degrees of the pole's elevation above 
the horizon of our place.... .And, by that means, 
the elevation of the pole, and consequently the 
latitude, of the place is known. 

E. Is there a star fixed exactly in the North 
pole, by which means you can know by sight 
where that pole is ? 

N. No : but there is a star of the second mag- 
nitude, about two degrees from the North pole, 
and it is called the Pole-star. And as the Earth's 
motion on its axis causeth an apparent motion of 
all the stars round the poles of the Heaven ; the 
pole-star appears to us to describe a circle, of 
four degrees diameter, round the pole itself, 
every twenty-four hours. And therefore, if we 
substract two degrees from the greatest observed 
height of the pole-star, or add two degrees to the 
least observed height thereof : the result gives 
the elevation of the pole at the place of obser- 
vation. 

As the North pole is elevated Sl\ degrees 
above the horizon of London, all those stars 
which are within 51 £ of that pole never set below 
the horizon of London. And therefore, if the 
greatest and least altitudes of any of these stars be 
taken with a quadrant, half the difference of these 
altitudes being added to the least, or substracted 
from the greatest, gives the elevation of the pole 
above the horizon. 

n 



And thus we can very easy and accurately find 
the Latitude of any place, by means of any star 
which never sets below the horizon of that place. 

The Latitude of ahv place mav also be found , 
by the Suits altitude at noon, on any day of the , 
year, quite independent of the stars..... I will first [ 
endeavour to shew you the reason of this, and 
then shew you the method. , 

The Equinoctial in the Heaven is directly over 
the Equator on the Earth. And just as many 
degrees as the Latitude of any given place is from 
the Equator, so many degrees is the point of the 
Heaven, which is over the place, from the Equi- 
noctial. Consequently, if \v r e can find how many 
degrees the point of the Heaven, which is directly 
over our place, is from the Equinoctial, we there- 
by find how many degrees our place is from the 
Equator ; or our Latitude. 

The Sun is in the Equinoctial twice every 
year ; namely, on the twentieth of March, and 
twenty-third of September ; and then he is di- 
rectly over the Earth's Equator. From the 20th 
of March to the 23d of September, the Sun is on 
the North side of the Equinoctial, and from the 
23d of September to the 20th of March, he is 
on the South side of it. The number of degrees 
that the Sun is from the Equinoctial, on any 
<day of the year, is called the Sun's declination 
for that day ; and is denominated North or 
South, as the Sun is on the North or South 
side of the Equinoctial.. ...So that, Declination 



. in the Heaven, Is the same as Latitude on the 

i Earth. 

There are tables reaofy calculated, which shew 

1 what the Sun's declination is, at the noon of every- 
day of the year ; as it is North or South on that 
day.. ...And the point of the Heaven which is di- 
rectly over any place, is ninety degrees above the 
horizon of that place. 

Now, to find the Latitude of the place, as sup- 
pose London, w r hich is on the North side of the 
Equator; observe the Sun*s altitude at noon, by- 
means of a quadrant, on any day of the year : and 
then, if, by the tables, you find the Sun's declina- 
tion to be North on that day, substract the decli- 
nation from the Sun's meridian altitude (that is, 
from his height at mid-day, as found by the qua- 
drant), and the remainder will be the height of the 
Equinoctial: which height being substracted from 
90 degrees, will give the Latitude of the place. 

Thus, on the 2ist of June, the tables shew us, 
that the Sun's declination is 23\ degrees North ; 
and if the Sun's altitude be observed with a qua- 
drant .on the noon of that day, the altitude will be 
found to be just 62 degrees. Now substract 23£ 
degrees from 62, and the remainder will be 38 \ 
degrees for the height or elevation of the highest 
point of the Equinoctial above the horizon of 
London ; which height being substracted from 
90 degrees, leaves remaining 51! degrees for the 
Latitude of London* 



( the Sun's declination be Se add its quaif- 

tity to the Sur/s observed altitude at noon, and 
the sum will be the elevation of the highest point 
of the Equinoctia *.*e the horizon of the place; 

which elevation being substracted from 90 de- 
grees, will leave a remainder equal to the Lati- 
tude of the place. 

Thus, on the 21st of December, the tables sh 
us, that the Sun's declination is 25 i degrees Sou: 
and if his altitude at noon be taken at London on 
that day by a quadrant, it will be found to be just 
15 degrees ; which being added to 23| degrees 
of South declination, gives 2S| degrees for the 
height of the Equinoctial, which height, being 
substracted from 90 degrees, leaves 51~ remain- 
ing for the Latitude of London, as before..... Bo 
you understand all this, Eudosia ? 

E. I think I do, en account of the reasons vou 

have given for the process But I will consider it 

bv and bv : and then tell vou if I find any diffi- 
culty. 

iVj Do so ; and now we will talk about the 
Longitude. The curve lines which you see 
drawn on the globe, from pole to pole (PLATE 
I. Fig* 1«J are called Meridians ; and each of 
them is a meridian to every place through which 
it passes ; because when it comes even with the 
Sun, by the turning of the globe on its axis, the 
Sun is then at the greatest height, as seen from 
all places on that meridian ; and consequentlv, it 
is then mid-day* or noon to each of them**.., 



89 

There are only 24 meridian semicircles on the 
globe, at equal distances from each other ; but 
we may suppose the whole spaces between them 
to be filled up with other such meridians, because 
every place, which is ever so little to the East or 
West from the meridian of any given place, has 
a different meridian from that of the given place. 
The whole circumference of the Equator is di- 
vided into 360 equal parts or degrees : and the 
English astronomers and geographers begin (what 
they call) the Longitude, at the meridian of Lon- 
don, and thence reckon the Longitudes of other 
places to the East or West, as the meridians of 
those places lie East or West from the meridian 
of London. So that the Longitude of any place, 
East or West of the meridian of London, is equal 
to the number of degrees intercepted between the 
meridian of that place and the meridian of Lon- 
don : according to the English way of reckoning'. 
Thus a meridian drawn through Copenhagen, in 
Denmark, would cut the Equator 13 degrees 
eastward of that point where the meridian of 
London cuts it ; and a meridian drawn through 
Philadelphia, in North America, would cut the 
Equator £4 degrees westward of the point where 
the meridian of London cuts it : and therefore 
we say, the Longitude of Copenhagen is 13 de- 
grees East from the meridian of London (which 
is termed the first meridian by the English) 
and the Longitude of Philadelphia, is 74 degrees 

West. 

H 2 



90 

Ail people, who know what Latitude and Lon- 
gitude meaiij reckon Latitude to begin at the 
Equator, that they may find the Latitude by the 
elevation of the pole above the horizon.. ...But r as 
they may begin the Longitude at the meridian of 
any place ; I suppose most nations reckon the 
Longitude of all other places from the meridian of 
the principal citj r of their own kingdom or nation. 

E* Why is it so difficult a matter to find the 
Longitude of any place, from the meridian of any 
other place, in comparison of finding the Latitude? 

N, Because we have a fixt point, or pole, in the 
Heaven, which shews us our Latitude by its ele- 
\ r ation above the horizon of our place : but there 
ii no visible meridian in the Heaven, to keep di- 
rectly over the meridian of any place on the Earth* 
If there were such a meridian, the Longitudes of 
all other places from it might be as easily found 
by its elevation above their horizons, as their 
'Latitudes are found by the elevation of the pole, 
or by the declination of the Sun from the Equator. 

E. I urderstand you perfectly well..,.. But, 
pray, what are the best methods that have been yet 
proposed for finding the Longitude ? 

N. The best method, in theory, is by a machine 
that will measure time exactly; so as to go as true 
at sea, as a good clock does on land. 

jE". Please to explain this. 

E. The Earth's circumference is 360 degrees ; 
and as it turns round its axis eastward every 
24 hours, it turns 15 degrees every hour: for, 24 



91 

times 15 is 3 GO. Therefore every place whose 
meridian is 15 degrees East of the meridian of 
London, will have noon, and every other hour, 
one hour sooner than it is so at the meridian of 
London. Every place whose meridian is SO de- 
grees eastward of the meridian of London will 
have noon, and every other hour, two hours soon- 
er than it is so at the meridian of London, and so 
on : the time always differing one hour for every 
15 degrees of Longitude. On the contrary* 
every place whose meridian is 15 degrees West 
from the meridian of London, will have noon, and 
every other hour, one hour later than it is so at 
the meridian of London ; and every place whose 
meridian is thirty degrees West from the meridian, 
of London, will have noon, and every other hour^ 

two hours later than it is so the meridian of 
London ; and so on. 

JE. Although this seems plain, I should be glad 
to have it illustrated by a figure. 

i\T. And here is one {Fig. 2. of PLATE III.) 
ready for you; in which let S be the Sun, abed 
ef, &c. the Earth, turning eastward round its axis> 
in 24 hours, according to the order of the letters. 
Let P be the North pole of the Earth, and a P, h 
P> c P, d P, &c. be as much of 24 meridian semi- 
circles as can be shewn in the figure, at 15 degrees 
distance from each other ; and suppose a P to be 
the meridian of London. 

Then, whichever side of the Earth is at any 
time turned toward the Sun, it will be day on 



92 

that side, and night on the other ; as expressed 
the light and shaded parts of the Earth in the 
figure. And, as it must be XII o'clock at noon 
on any meridian which is turned toward the Sun 
at any moment of absolute time, because that 
meridian will then be in the middle of the en- 
lightened half of the Earth, as on the meridian 
P a ; it is plain that it will be twelve o'clock at 
night, at the same instant, on the opposite meridi- 
an n P, because it is then in the middle of the 
dark ; VI o'clock in the morning on the meridian 
t P, and VI in the evening on the meridian £* P ; 
and so, all the intermediate hours, on the inter- 
mediate meridians, at the veray instant when it is 
noon on the meridian P a* So that, supposing P 
c to be the meridian of London, it is plain, that 
when it is XII o'clock there, it will be I o'clock 
in the afternoon on the meridian P b 9 because 
that meridian is past by the Sun, 15 degrees, or 
one hour to the eastward ; II o'clock in the after- 
noon on the meridian Pc: III o'clock on the 
meridian Pd; and so on. But it can only be 
XI in the forenoon, on the meridian ?2, when 
it is noon on the meridian Pa; because* P z is 
then an hour short of being even with the Sun : 
X o'clock in the forenoon on the meridian P y ; 
because that meridian wants two hours of being 
even with the Sun, and so on. 

Now, as every master of a ship knows how to 
find the time of the day at the place of his ship ? 



93 

hy the height of the Sun ; or the time of the 
night by the height of any given star that revolves 
at a good distance from either of the celestial 
poles ; if he first finds the Latitude of the place 
of his ship : he may find the Longitude of that 
place in the following manner, if he can depend 
upon the true going of his watch. 

Before he sets out from any port, as suppose 
from London, let him set his watch to the exact 
time at that port ; and then, let him sail where he 
will, his watch will always shew "him what the 
time is at that port from which he set out. 

Nov/, suppose him to he at sea, on his way to 
the West-Indies; and that he has sailed from Lon- 
don at a ss far westward as », and then wants to 
find the Longitude of the place of his ship at x. 
He first finds the Latitude of the place #, and then, 
by the altitude of the Sun, finds the time at that 
place, which we shall suppose to be IX o'clock in 
the morning: he then looks at his w r atch, which 
shews the time at London, on the meridian Pa; 
and Snds that it is XII o'clock at noon on the 
meridian of London. By this he knows, that he 
is three hours to the West of London; and as 
every hour of time answers to 15 degrees of Lon- 
gitude, he finds that the meridian of the place of 
his ship is 3 times 15, or 45 degrees West from 
the meridian of London. And, as- every hour 
answers to 15 degrees of Longitude, so every four 
minutes answers to one degree. If he had been 
as far eastward (as at d) from the meridian of 



94 

London, he would have found it to be III o'clock 
in the afternoon at the place of his ship, when his 
watch would have^shewn him that it was then on- 
ly mid-day at London ; and so, in that case, he 
would have known that the Longitude of his ship 
was 45 degrees East from the meridian of Lon- 
don. 

£. This appears to me to be a very rational and 
easy method of finding the Longitude, if a watch 
can be made that will keep exact time at sea.... 
Pray, has there ever been such a watch made, so 
as that it can be depended upon ? for otherwise I 
should think it very dangerous ; because, for eve- 
ry four minutes that it would either gsin or lose, 
it would cause an error of a whole degree in rec- 
koning the Longitude. 

N. Mr. Harrison has succeeded the best of any 
who has ever yet attempted to make such a watch* 
But that watch has been found not to keep time 
quite so exactly as was expected, after some 
months trial at the Royal Observatory at Green- 
wich. Yet it must be acknowledged that* Mr. 
Harrison has very great mtrit, and deserves the 
reward he has got for his ingenuity: and many are 
of opinion, that he can still make a watch that will 
measure time more exactly than the one which 
has been already tried (and for which he has got 
the reward,) as it is the only one he ever made. 

Another method (and which is a very sure 
one) for finding the Longitude, has been practised 
for many years : and that is, by the eclipses of Ju- 



95 

piter's satellites ; but it is attended with two i 
conveniences ; first, as it requires the telescope to 
be quite steady, by which those eclipses are ob- 
served, it cannot be put in practice at sea, on ac- 
count of the unsteadiness of the ship : and second- 
ly, no observations of these eclipses can be made 
in the day-time, because Jupiter is not then visi- 
ble. 

£. But I should think it must still be very use- 
ful in finding the Longitudes of places on the land, 
where the telescope may be kept quite steady..—. 
Pray, explain the method by which the Longitude 
"has been thus found. 

N. The English astronomers have calculated 
tables which shew the times of those eclipses, all 
the year round on the meridian of London ; and 
the French have done the like for the meridian 
of Paris..... Now, suppose an Englishman to be at 
Kingston in Jamaica, and that he observes either 
of Jupiter's moons to be eclipsed jtist at One 
o'clock in the morning: he looks at the tables, to 
see at what time the same eclipse is on the meri- 
dian of London ; and finds the time there to be at 
8 minutes after VI in the morning. The differ- 
ence of the times, as reckoned at London and at 
Kingston in Jamaica, is thus found to be 5 hours 
8 minutes, or 308 minutes ; which being divided 
by 4 (because 4 minutes of time answer to one 
degree of Longitude,) quotes 77 for the number 
of degrees by which the meridian of Kingston is 
west from the meridian of London : and thus he 



finds, that Kingston is in 77 degrees of West 
Longitude from London. 

E. You have explained these matters very ful- 
ly ; and I thank you for it. 

N. I thought to have done it in much fewer 
words ; and am afraid I have quite tired you this 
morning, as you cannot be very well after having 
such a bad night. 

N. But I am quite well now, brother; and you 
have finished in very good time, as the bell ji 
rines for breakfast. 






DIALOGUE VI 



OK THE CAUSES OF THE DIFFERENT LENGTHS OF 
DAYS AND NIGHTS, THE VICISSITUDES OF 
SEASONS, AND THE VARIOUS PHASES OF THE 
MOON,. 



:o^ 



Meander* I AM very glad to see you so early 

this morning, Eudosia I hope you rested well 

last night, and had no return of your late com- 
plaint. 

Eudosia. I slept very well from ten o'clock till 

, five ; and am quite well. 

N. I am very glad to hear it. What subject 
I do you propose for us to enter upon, this mora- 

E. I should be glad to know the reason why 
the days and nights are of different lengths at dif- 
ferent times of the year. For, although it is plain, 
that the turning of the earth round its axis once 
every twenty-four hours, must cause a continual 
succession of day and night in that time ; ths 

x 



98 

kame as if the Earth were at rest, and the Sun 
moved round it in 24 hours ; I do not understand 
the reason why the days and nights are continual- 
ly varying in their lengths, unless it were by a 
particular motion of the Sun northward and south- 
ward, across the Equator, in a year But, from 

what you have already told me, it appears plain, 
by the stated laws of nature, that the Sun cannot 
have any such motion, 

JV. Indeed he cannot.... And you shall soon see 
the reason of the different lengths of days and 
nights, and of all the four seasons of the year, 
without any motion of the Sun northward and 

southward across the equator Please to light 

that candle, by way of a Sun, and set it upon the 
table, whilst I shut the windows ; so that we may 
have no light in the room but from the candle. 
-E. There it is, brother. 

iV r . NoVi r , I put a^ wire axis through oiif small 
three inch globe, so as to reach a little way out 
frbm its surface in its North and South Poles..... 
I move the globe round the flame of the candle, 
keeping it always at the same height from the ta- 
ble, and its axis perpendicular to the table : and 
you see that the candle is always even with the 
Equator of the globe, and enlightens it just from 
pole to pole. 
E. Exactly so. 

N. And that one half of the globe is enlight- 
ened by the candle, whilst the other half is not : 
and consequently, that it appears as if it were dayr 



99 

on the side of the globe next the candle, and night 
on the opposite side. 

E. Very plain. 

JV. I now turn the globe round its axis many 
times during the time I move it round the candle 
as before ; and you see that every part of its sur- 
face, from the North Pole to the South, goes 
equally through the light and shade. So that, if 
the globe was turned round its axis once every 
24 hours, and carried round about the candle once 
in a year, every point of its surface from pole to 
pole, would be twelve hours in the light, and 
twelve hours in the dark. 

E. Undoubtedly it would. 

iV. Then, you see, that supposing the candle to 
have no motion from one side of the equator to 
the other, and the axis of the globe to keep per- 
pendicular to its orbit, and its whole course round 
the candle, the days and nights could never vary 
in their length* 

E. Self-evident. 

N. I now incline the North pole of the axis a 
little toward the candle, and turn the globe round 

its axis You now see that the candle shines as 

far over the north pole as the axis of the globe is 
inclined toward the candle ; and that all those 
places of the northern hemisphere which go 
through the dark, go through less of it than they 
do of the light; so that their days are longer than 
their nights ; and the candle, being on the North 
side of the Equator, shines as far short of the 



100 

South pole as it shines over the North pole : and 
consequently, all the places on the southern hem- 
isphere of the globe, which go through the light* 
go through a less portion of it than they do of the 
dark ; and so have their days shorter than their 
nights. 

But make the North pole of the axis decline 
from the candle, and turn the globe round its axis ; 
the candle will not enlighten the globe to the North 
pole, but it will shine round the South pole. And 
now, all the noithern places of the globe which go 
through the light, go through less of it than they 
do of the dark ; so that the days are shorter than 
the nights on the North side of the Equator, and 
the contrary on the South side of it. You now 
see, that turning the poles of the earth alternately* 
more or less, toward and from the Sun, will have 
the same effect, as if the Sun really moved north- 
ward and southward, to different sides of the 
Equator. 

E. It will, indeed. But do the poles of the 
Earth incline toward the Sun, and from him, in. 
that manner, at different times of the year ? 

N. They do : and here is a figure, (PLATE 
IV. Fig*. 1.) by which the whole of that matter 
may be very easily explained. 

Let ABCD E F G HA represent the Earth's 
orbit (seen obliquely, which causeth it to appear 
of an elliptical shape.) And let /be tha Earth, 
going round the Sun S 9 according to the order 
the letters. A B C D> &c. once every year. 




Cray & Todd se. 



101 

Now, suppose a great circle P u I p x, to be 
drawn round the Earth, through its North pole P 
and its South pole/?; and let ^ be the Equator. 

Divide the great circle P u I p x into 360 equal 
parts or degrees : and set off 23i of these degrees 
from P to U. Then at the distance P u from the 
North pole, draw a circle all around it ; which 
call the North polar circle : and suppose just such 
'another circle to be drawn round the South pole. 
Make the Earth's axis P p incline 23| degree^ 
toward the right hand side of the plate ; and let 
the Earth /be carried round the Sun S y in the or- 
bit A&C D, &c. in the time of its turning 365| 
times round its axis : and, in its whole course, 
let its axis Pp still incline 23^ degrees toward the 
right hand side of the plate. 

Then it is plain, that wh«n the Earth is at i, the 
whole North polar circle fall within the enlight- 
ened part of the Earth ; and all the northern 
places between the equator ^ and the North po- 
lar circle u are more in the light than in the dark x 
and therefore, as the Earth turns round its axis, 
these places will have longer days than they have 
nights : and the Sun will point as far North of tha 
Equator ^as shewn by the straight line i?, as he 
shines round the North pole P ; for the distance 
^ T, northward from the Equator, is equal to 
the distance P u from the North pole ; which is 
23| degrees... •.This is the Earths position on the 
21st of June, when our days are at the long^st^ 
and nights at the shortest. 

I % Ma*. 



102 

At the distance i^ T (231 degrees northward 
from the Equator) describe the circle T, round 
the globe, parallel to the Equator : and as the Sun 
is directly over the circle T, in the right line P y 
and can never be farther North of the Eauator ; 
but begins then to recede, as it were, southward 
from the circle 7\ that circle is called the Northern 
Tropic, or limit of the Sun's greatest North de- 
clination from the Equator §>. 

As the Earth moves on in its orbit from I to K 
its axis P p inclines more and more sidewise to 
the Sun S; as it still keeps parallel to the position 
it had when the Earth was at /.• for which reason^ 
the northern places are gradually turned away 
from the Sun ; and their days grow shorter, and 
their nights longer. 

When the Earth is at £, its axis P p inclines 
neither toward the Sun nor from him, but is side- 
wise to him : so that the Sun is then directly over 
the Equator, and enlightens the Earth just from 
pole to pole. And, as the Earth's rotation on its 
axis then carries all the parts of its surface between 
the poles equally through the light and the dark, 
the days and nights are equally long at all places 
of the Earth. This is the Earth's position on 
the 23d of September* 

As the Earth advances from K to Z, through 
the part C D of its orbit, the North pole P and 
all the northern places of the Earth are gradually 
more and more turned away from the Sun S: and 
those places of the northern hemisphere which go 



103 

through the light and the dark go through more of 
the dark than of the light; so that their days be- 
come gradually shorter and their nights longer. 

When the Earth comes to L in its orbit, its 
North pole P is as much turned away from the 
Sun S, as it was turned toward him when the 
Earth w r as at J: and therefore, when the Earth b 
at Z, the whole north polar circle u is in the dark ; 
and the Sun points 23r degrees (as shewn by the 
right line r) to the South of the Equator §>j and 
is then over the circle t, which is parallel to the 
Equator, and is called the Southern Tropic, be- 
cause it is the utmost limit of the Sun's South de- 
clination from the Equator. This is the Earth's 
position on the 21st of December, when all those 
places in the northern hemisphere, which go 
through the light and the dark, go through the 
least portion of the light, and the greatest of the 
dark, that they can do on aay day of the year* 
And therefore, the days are then at the shortest, 
and nights are at the longest, in the northern half 
of the Earth, all the way from the Equatur ^ 
to the north polar circle u; within which circle 
there is no day at all. 

As the Earth advances from L to 31, through 
the part E F of its orbit, its axis Pp is gradually 
more and more turned sidewise to the Sun; the 
northern places fall more and more into the light, 
and their days lengthen and nights shorten. And 
when the Earth comes to M, which is on the 20th 
of March, its axis neither inclines toward the Sun 



104 



nor from him, but sidewise to him. And then, 
the Sun is directly over the Equator £Q and en-' 
lightens the Earth from its North pole P to its 
South pole p; and as it turns round its axis, every 
place on its surface from pole to pole goes equal- 
ly through the light and the dark ; and has the day 
and night of an equal length, that is twelve hours 
each. 

Lastly, as the Earth goes on from 31 to 7, in tne 
r:art G H'oi its orbit, its North pole P, and all its 
northern places from the Equator ^to that pole, 
advance gradually more and more into the light j 
and so, have their days longer and nights shorter, 
till the Earth comes to I on the 20th of June, 
when the days in those places are at the longest, , 
and nights at the shortest ; because they incline 
the most to the Sun that they can do on any day 
of the year ; and consequently they then go through 
the greatest portions of the light, and the least of 
the dark, all the way from the Equator to the> 
North polar circle u; within which circle there 
is then no darkness at all. 

And thus, as the Earth's axis still inclines to- 
ward one and the same side of the heavens, in its 
whole annual course round the Sun; as in the 
figure it does toward the right hand side of the 
plate ; it is evident, that its axis must incline con- 
stantly, more or less, toward the Sun during our 
summer half of the year ; and more or less from 
him during our winter half. That, when it is 
summer in the northern hemisphere, it must be? 



10S 



winter m the southern, and the contrary : and that 
there can be no difference of seasons at the Equa- 
tor, because it is in the middle between the poles, 
and always equally cut in halves by the boundary 
cf light and darkness u x. 

E. This very plainly shews the reason of the 
different lengths of days and nights, and also of alt 

the variety of seasons But, as I apprehend the 

matter, each pole, in its turn, must be continually 
in the light for half a year together ; and in the 
dark for the other half : so that it appears there 
can be but one day and one night at each pole, in 

the whole year. 

N. You are quite right, Eudosia : and have told 
me the very thing that I was about to inform you 

° E. I came into your room yesterday about one 
o'clock ; but you happened to be out : and seeing 
a book lying open on your table, I looked into it; 
and found mention made of the ecliptic, the signs 
thereof, and the Sun's place. Pray what is the 
ecliptic, and what are its signs? 

N. If the plane of the Earth's orbit were pro- 
duced out to the stars, like a broad circular thin 
plate, its edge would form a great circle among 
the stars ; which great circle (though only an im- 
aginary one) we call the Ecliptic. And as the 
Earth moves in the plane of such a circle, in its. 
whole course round the Sun, it will be always 
seen from the Sun as moving in such a circle 
synong the stars ; and, at any given time, in tho 



106 

opposite point of that circle to the point of it in 
which the Sun then appears as seen from the 
Earth. So that, as the Earth goes round the Sun 
once a year, the Sun will appear to us to describe 
a great circle among the stars, in a year. 

Astronomers divide this circle into twelve equal 
parts, called Signs, and each sign into 30 equal 
parts called Degrees. And in whatever Sign and 
Degree the Earth would appear, as seen from the 
Sun at any given time ; the Sun must then ap- 
pear in the opposite Sign and Degree as seen 
from the Earth : and the part of the Ecliptic in 
which the Sun's centre appears to be, as seen 
from the Earth at any given instant of time, is 
called the Sun's place in the Ecliptic, at that time* 

These Signs are called Aries, Taurus, Gcinini, 
Cancer, Leo, l r trgo, Libra, Scorpio, Sagittarius, 
Capricornus, Aquarius, and Pisces* The month 
and days of the year, in which the Sun appears to 
enter these Signs, are as follows : 

Aries, Taurus, Gemini, Cancer, Leo, Virgo, 
March April May June July August 
20 20 21 21 23 23 

Libra, Scorpio, Sagittarius, Capricornus, Aquarius, Pisces, 

Sept. Octob. Novemb. Decern. Jan. Feb. 
23 23 22 21 20 19 

jE. Then, let me see ; I think I could tell, by 
this, what the Sun's place in the Ecliptic is, on any 
day of the year. Each sign has 30 degrees ; this 
is the 11th day of July, and the Sun does not en- 
ter Leo, till the 23d -, so that he must vet be in 



toy 

Cancer, ^ake 11 from 23, and there remains 
12, so that the Sun is now 12 degrees short of 
the last point of Cancer ; and consequently he is 
in the i8th degree thereof* 

N. You are perfectly right, sister : and I think 
we have done with this part of our subject. 

E. And will you allow me this morning, to' en- 
ter upon any other ? 

jV. Why not ? and continue it too till the bell 
calls us to breakfast. 

E. Which, I hope, will not be in less than half 

ail hour ; and till then, I should be glad to learn 
something about the Moon. 

N. Very well : it is your province to ask ques- 
tions, and mine to answer them. 

E n What is the cause of the Moon's appearing 
of such different shapes as she does to us every 
month, always increasing from change to full, 
and decreasing from full to change? 

N. Be pleased to light the candle again, and set 
it on yonder table, at the farther end of the room, 
whilst I close the window- shutters. And then, 
do you stand at a good distance from the candle, 
and look toward it. 

E. Very well, brother..... Now. 

N. Here is a small ivory globe, with a wire 
through it> by way of an axis. I will now move 
that globe round your head ; and, as I carry it 
about, do you turn yourself round, and keep look- 
ing at it. Let the candle represent the Sun, your 
head the Earth, and the globe the Moon* As 



108 

the candle can enlighten only that half of the globe 
which is turned toward it, so the Sun can only en- 
lighten that half of the Moon which is at any time 
turned toward him. The other half is in the dark, 
and the Moon goes round the Earth in her orbit 
once n month* 

As I carry the globe round your head, the dark 
side of it is toward you when it is between your 
head and the candle ; the light side when it is 
carried half round or opposite to the candle with 
respect to your head ; and in the middle between 
these two positions, you have half the light and 
half the dark side toward you. 

E. Very true..... And when the globe is betwen 
me and the candle the whole of its enlightened 
side disappears : when you move it a little way 
from that position, I see a little of its enlightened 
side, appearing horned, like the Moon when she 
is a few days old» When you carry it a quarter 
round, I see half its enlightened side, which ap- 
pears just like the Moon when she is a quarter 
old» As you move it farther onward I see more 
and more of its enlightened side ; and it continues 
to increase like the Moon, till it is just opposite 
to the candle, when I see the whole 6i its enlight- 
ened side ; and then it appears quite round, like 
the full Moon. After which, I see less and less 
of its enlightened side, which gradually decreases 
like the Moon, until you bring it again between 
me and the candle ; and then, the whole of its en- 
lightened side disappears, as before. 



I 109 

iV. And doth not this shew very plainly, why 
the Moon must appear to us to increase from the 
change to the full; and decrease from the full 
to the change. 

E m Very plainly, indeed : and, I think, it also 
shews that the Mocn does not shine by any light 
of her own; but only by reflecting the Sun's light 
that falls upon hen For if she shone by her own 
light, we should always see her round, like the 
Sun, 

jV. That is a very good and just observation^ 
sister ; and it is a remark that I might possibly 
have forgotten to make. 

E* But, if you had not explained the different 
appearances of the moon by means of a globe and 
a candle ; how would you have done it by a figure? 

iV. Here is a figure for that purpose (PLATE 
IV. Fig. 2.), in which, let S represent the Sun, E 
the Earth, Mthe Moon ; and abed efg h a the 
Moon's orbit, in which she goes round the Earth 
from change to change, according to the order of 
the letters ; that is, eastward in the heavens ; al- 
though the Earth's daily motion round its axis 
the same way T being quicker than the Moon's 
progressive motion, makes her appear to go round 
westward. When the Moon is at M 9 between the 
Earth and the Sun, her dark side is then toward 
the Earth ; and she disappears, because that side 
reflects ao light. When she is at iV, a little of her 
enlightened side will be seen from the Earth : and 
then she will appear horned, as at n* Wi*en she is 

K 



lid 

at O y half her enlightened side will be toward the 
Earth, and she will then appear as at o, or in her 
first quarter, being then got a quarter of her orbit 
out from between the Earth and the Sun. When 
she is at P, more'thanhalf of her enlightened side 
is toward the Earth; and she appears (what we 
call) Gibbous, as at p. When she is opposite to 
the Sun, as at .£?, the whole of her enlightened side 
is toward the Earth : and she appears round and 
full, as at q. 

E. Let me interrupt ycu a little here. Pray 
how can the Sun shine upon the Moon, when the 
Earth is directly between her and the Sjan ? For, I 
should think, that the Earth would stop the Sun's 
light from going to the Moon. 

2\, It does sometimes ; and then the Moon is 
eclipsed; and sometimes the moon comes direct- 
ly between the Earth and the Sun at the time of 
her change ; and then we say, the Sun is eclipsed. 
But we shall talk of these matters afterward, 

E* I am very glad of it ; and now, Sir, pray, 
proceed. 

N. When the Moon is at i? in her orbit, part of 
her enlightened side is turned away from the 
Earth ; and she appears gibbous again, as at r. 
When she is at T (three quarters round her orbit 
from between the Earth and the Sun) half of her 
light and half of her dark side is toward the Earth; 
and she appears half decreased, or in her third 
quarter, as at t. When she is at U in her orbit; 
the greatest part of her enlightened side is turned 



Ill 

away from the Earth ; and she appear horned, 
as at iu And when she is between the Earth and 
the Sun again, as at M, she is quite invisible ; be- 
cause the whole of her unenlightened side is then 
toward the Earth. 

E. This does very well ; but I like the candle 
and ball still better. 

N. For this very good reason, that they are 
more like the works of nature than any figures 
we can draw on paper. 

E. How long is the Moon in going round her 
orbit from change to change ? 

N. Twenty-nine days, twelve hours, forty-four 
minutes, three seconds. 

E. And what is her distance from the Earth's 
center ? * 

N. Two hundred and forty thousand English 
miles. 

E. How many times would it take round the 
Earth to go round the Moon's orbit ? 

N. Sixty times : and therefore, every degree of 
the Moon's orbit is equal in length to 60 degrees of 
a great circle (or 4155 miles) on the Earth's surface, 

£• What is the Moon's diameter ; and in what 
proportion is it to the Earth's ? 

JV. The Moon's diameter is 2183] miles; and 
it is in proportion to the Earth's diameter as 100 
is to 365, or as 20 to 73. 

E. What are those spots which we see on the 
Moon? I think I have hear J some people .say 
that they are seas. 



11 

y. So they were thought to be before there were 
food telescopes to view the moon by. But now 

they are found to be only darker places of the land 
in the Mood, which do not reflect the Sun's light 
so copiously as the whiter parts do. For we sec 
they are full of pits and deep valleys : but if they 
were seas, they would have even and smooth 
surfaces. 

E. So they certainly would, brother. But as it 
may be known by these spots whether the Moon 
turns round her own axis or not;. ...If she does turn 
round I should be glad to know in what time ; be* 
cause I should thereby know the length of her 
days and nights. 

N. She turns round her axis exactly in the time 
she goes round her orbit ; and this we know by her 
keeping always the same side toward the Earth. 
E. Then she can have only one day and one 
night between change and change, or in 29 days* 
12 hours, 44 minutes, 3 seconds of our time. 
JV. Exactly so. 

JE« And is her axis inclined to her orbit, as our 
Earth is to its orbit ? 

L. No : her axis is perpendicular to the ecliptic^ 
in which the Earth moves ; and nearly perpendi- 
cular to her own orbit. 

E. Then her days and nights must always be 
equally long ; and she can have no different sea- 
sons ? 

You are very right, Eudosia* 



113 

^VBut pray, brother, how is it possible that we 
can only see one and the same side of the Moon 
at all times, if she turns round her axis?.. ..For, I 
should think, that it she has such a motion, we 
inust see all her sides. 

.A 7 . Take up that little globe by its axis, between 
your fore finger and thumb. 
E. There it is. 

A 7 . Now, hold its axis, without turning (as you 
hold your pen when you write), and carry it 
round the ink-horn on the table. 
E. I do. 

N. And do you not see r that as you carry the 
globe so round, without turning it at all on its 
axis, all its sides are successively shewn to the 
inkhorn ? 

E* They are indeed. ' 

JY r . Carry it round the ink-horn agaia ; and try 
whether you can make it still keep one and the 
same side toward the ink-horn, without turning 
round on its axis, by turning the axis round be- 
tween your fore-finger and thumb. 

jB. I find it impossible to do so :..... for in each 
revolution of the globe about the ink-horn in order 
to make the globe keep still the same side toward 
it, I am obliged to turn the axis once round be- 
twixt my finger and thumb : and, as the axis is 
fixed in the globe, I cannot turn the axis round 
without turning the globe round too» 

JV. Well, sister, seeing that the Moon goes 

round the Earth in her orbit, as you carry the 

k 2 



t!4 

globe round the ink-horn ; is not her keeping the 
same side always toward the Earth a full proof of 
her turning round her axis ? 

E. It certainly is : and I can also see that as the 
Sun is on the outside of the Moon's crbit, her 
keeping always the same side toward the Earth, 
makes her shew herself all around to the Sun be- 
tween change and change For, in the time that 

I carried the globe round the ink-horn, and kept 
always the same side toward it ; you, who were 
on the outside of the circle in which I carried 
the globe so round, saw all its sides. 

^V. You are very right Bat I am sorry to 

hear our breakfast-bell: for we have net yet done 
with the Moon, 



US 



DIALOGUE VII. 



on Tira moon's motion bound the earth ane 

SUN ; AND THE ECLIRSEs OF THE SUN AND MOON. 



:o: 



Meander. SO, sister; if yesterday had not been 
Sunday, I believe you would not have given 
yourself that day's rest from your astronomical 
studies, 

Eudosia. To me, brother, these studies are re* 
creations, which I esteem better than bare rest...* 
And, on Sunday we rest not ; but are better em- 
ployed in the duties of the day, than we generally 
are on all the other days of the week. 

N. True ; and therein our duty is closely con- 
nected with our interest. Shall we now resume 
our subject about the moon? as I told you, last 
Saturday mornings that we had not done, witin 
her. 

£. If you please, Sir* 



' 116 

JV". Then you must always start the game ; and 
when that is done, we will pursue it. 

E. I think the Moon would always appear full 
as seen from the Sun, if she were big enough to 
be seen by an observer placed on the Sun's sur- 
face. 

iV. She certainly would ; because whichever 
side of her is turned tpward the Sun at any time, 
that side would be fully enlightened by the Sun, 

E. And I imagine, that if an observer were 
placed on the side of the Moon which always- 
keeps toward the Earth, the Earth would appear 
to him in all the different shapes that the Moon 
does to us. Only, that when the Moon is new 
to us, the Earth would be full to the Moon ; and 
when the Moon is full to us, the Earth would dis- 
appear, or be new to the Moon. 

N. What reason have you for thinking so, Eu- 
dosia? 

E. Because, whichever side of the Earth or 
Moon is turned toward the Sun at any time, that 
side is then enlightened by the Sun. And there- 
fore, when the dark side of the Moon M (Fig. 2. 
of PLATE IV.) is toward the Earth is, the en- 
lightened side of the Earth is then fully toward 
the Moon ; and must appear to her like a great 
full Moon. And when the enlightened side of 
the Moon at ^ is fully toward the Earth, the dark 
side of the Earth is toward the Moon ; and there- 
fore it cannot appear to the moon, as the moon at 
jft/does not appear to us. And farther, when ths 



117 

Moon appears half full to us (or in her first quar- 
ter) at O y the Earth must appear half decreased 
to the moon, being then half way between its full 
and change, as seen from her. And lastly, when 
the Moon is in her third quarter at T 7 as seen 
from the Earth, the Earth must appear as in its 
first quarter to the Moon ; it being then the mid- 
dle time between the new and full Earth, as seen 
from the moon. 

N. You are exactly right, sister : and as the sur- 
face of the Earth is lii times as large as the sur- 
face of the Moon, when the Earth is full to the 
Moon, its surface appears 13 times as big to the 
Moon, as the surface of the full Moon does to 
us, 

E. If the moon be inhabited on the side which 
always keeps toward the Earth, I think these in* 
habitants may as easily find their Longitude as 
we can find our Latitude. 

N. Tell me how : and if you can make that 
out, I shall say you think very well. 

E. When you explained the Longitude to me, 
vou made me understand, that if there were a 
visible meridian in the Heaven, keeping always 
over one and the same meridian on the Earth 
(which it would do if it revolved eastward in 24 
hours as the Earth does,) the Longitude of any 
other meridian of the Earth from that meridian, 
might as easily be found as the elevation of the 
pole above the horizon is found. Now, seeing 
that the Moon keeps always one and the same 



118 

side toward the Earth, it is plain, that the Earth 
will be always over an observer's head who is on 
that part of the Moon-s surface which seems to 
us to be her center. And therefore if Longitude 
on the Moon were reckoned from the meridian of 
that observer, those on all her other meridians on 
the same side, might find how many degrees lie 
between their meridian and that which is under 
the Earth, by observing how many degrees the 
Earth is East or West of their meridian. But, 
as those inhabitants who live on what we call the 
back of the moon, never see the Earth ; they are 
deprived of that easy method of finding their 
Longitude. 

iV. Truly, sister, I ought to make you a very 
fine speech for that thought: but having no talent 
that way, all I shall say is, that I am very well 
pleased by it. 

jE. I am very glad to hear you say so, because 
you thereby assure me that I am right.. ..But now 
a difficulty occurs to my mind, which I beg you 
will remove. 

JV. Only tell it me, and I will remove it if I can. 

£• The Moon goes round the I^arth every 
month ; and as the Earth goes rouncj, the Sun in a 
year, the Moon must do so too. How happens 
it, that the Earth, by moving at tl>e rate of 68,000 
miles every hour, in its orbit, does not go off, and 
leave the moon behind ? 

N* The moon is within the sphere of the 
Earth's attraction : and therefore, let the Earth 



119 

tove in its orbit as fast as it will, the Moon must 
accompany it* For you know if you put a peb- 
ble into a sling, and whirl it round your head, the 
pebble will go round and round your head, whether 
you stand still in one and the same place, or whe- 
ther you walk directly forward, or go round the 
circumference of a large circle. And the ten- 
dency of the pebble to fly off, and the force with 
which you hold the string to confine the pebble 
in its orbit, will be the same in one case as in the 
other. 

E. I thank you, brother, for having set me right 
in this matter ; and at the same time for convincing 
me, by the simile, that the Moon's centrifugal 
force, or tendency to fly off out of her orbit, is 
equal to the power with which the*Earth attracts 
her, and thereby retains her in her orbit : for, if 
her centrifugal force were greater than the Earth's 
attraction, she would fly out of her orbit, and so 
abandon the Earth. And if her centrifugal force 
were less than the power by which the Earth at- 
tracts her, she would come nearer and nearer the 
Earth in every revolution, and would fall upon it 
at last. 

J\\ I find, dear Eudosia, that you very seldom 
need to be set right : and when I do, you always 
improve upon it, by making farther observations* 

E. By the last figure you explained, it would 
seem, that the Moon goes just round her orbit be- 
tween change and change. But I think, that as 
both the Earth and Moon £o round the Sun in a 




Gray X- Ttdds*. 



120 

year, the Moon must not only go round her orbit 
between change and change, but even advance as 
many more degrees as the Earth has moved in 
its orbit during that time, in order to be again in 
conjunction with the Sun. For, in whatever part 
of the dial-plate of my watch, I find the hour and 
minute-hands in conjunction, I observe that the 
minute-hand must go as much more than round 
to the same point again, before it overtakes the 
hour-hand, as the hour-hand advances in the inter- 
val between its last conjunction with the minute- 
hand and its next. 

JV". You are very right ; and your inference from 
the hour-and rninute-hands of the watch is full as 
good as mine from the pebble and sling. I drew 
a figure last Saturday afternoon, in order to explain 
this matter to you by it. But, as you understand 
the thing so well already, we have no occasion for 
the figure. 

E. Nay, brother,....I beg you will shew me the 
figure, and explain it too, if your time will per- 
mit. 

N. Then, here it is: (PLATE V, Fig. 1.) 
Let AB CDF FGbe one half of the EartWs 
orbit ; which will do as well for us, just now, as 
if the whole of it had been drawn. Let iS* be the 
Sun, a the Earth, h the Moon when new, or be- 
tween the Earth and the Sun ; and i k /the Moon's 
t>rbit, in which she goes round the Earth accord- 
ing to the order of the letters h i k I : and let the* 



121 

Earth together with the Moon in her (imaginary) 
orbit, go round the sun in a year. 

Draw a diameter k h of the Moon's orbit, when 
the Earth is at a ; so as, if that line were con- 
tinued, it would go on straight to the Sun's cen- 
ter S : it is plain, that when the Moon is in the 
end h of that line, she must be new, or between 
the Earth and the Sun. 

As the Earth moves on, from a to &, from b to 
e, from c to d, from d to e, &c. the said diameter 
k h, k h, k h y k A, will still continue parallel to the 
position k A, that it had when the Earth was at a: 
that is, it will always keep perpendicular to the 
bottom line H I of the plate. And therefore, if 
it pointed once toward a fixed star, whose distance 
from the Sun is so great, that the whole diameter 
of the Earth's orbit bears no sensible proportion 
to that distance, (which is really the case), the 
point h would always keep between the Earth and 
the same star. 

-B. I understand you very well : but, do you 
say the stars are fixed P 

N* I do say so ; and will convince you after* 
ward that they are* 

jB. I beg pardon for interrupting you so often. 
•...Pray, now proceed. 

N. In the time the moon goes round from h to h 
again, in the direction hi A I A,*she goes quite round 
her orbit ; which she would always do between 
change and change, if the Earth always remained 
at a. 



122 

But as the Earth advances as far in its orbit as 
from a to £, between any change of the moon and 
the next that succeeds it ; it is plain, that when the 
Earth is at b and the Moon new at m, she will have 
gone more than round her orbit from h to h a- 
gain, by the space h nu And as all circles, be they 
so great or ever so small, contain 360 degrees (a 
degree being not limited by any certain number of 
miles, but the length of the 360th part of a circle) 
the space h m y by which the Moon has gone more 
than round her orbit, from her change at h to her 
change at at-, will contain just as many degrees 
and parts of a degree, as the Earth has moved in 
that time, from a to b in its orbit. 

At the second change of the Moon from h, the 
Earth will be at c, and the Moon at n: by which 
time she will have gone twice round her orbit from 
h to h again, and as much more as the space or part 
h n of her orbit contains, which consists of as many 
degrees as the part a b c of the Earth's orbit does. 
...And so on, through the whole figure. 

-£"• I see all this very plainly ; and that the figure 
includes six changes of the Moon, as from h to in 
from m to rc, from n to 0, from to p, from p to y, 
and from q to r....But, at the last of these changes, 
it seems (by the figure) that the Earth has not 
gone half way round the Sun : for the last line 
of conjunction S rg is not quite even with the 
first line of conjunction a h S. 

iV. Nor should it be ; for if it be rightly drawn 
(and I find I must take care how I draw figures 



123 

for you), it must want 5^ degrees of the Earth's 
progressive motion in half a year. For six courses 
of the Moon, from change to change, contain only 
177 days, 4 hours, 24 minutes, 18 seconds, which 
wants 5 days, 7 hours, 35 minutes, 42 seconds, of 
182 days, 12 hours, which is the half of a common 
year* And, in that difference of time, the Earth 
moves somewhat more than Rve degrees in its 
orbit. 

E. I remember you told me that the time from 
change to change is 29 days, 12 hours, 44 minutes, 
3 seconds : pray in what time does the Moon go 
round her orbit ? 

JV. In 27 days, 7 hours, 43 minutes, 5 seconds. 

E. And how far doth the Earth move in its or- 
bit between change and change of the Moon ? 

JV. Twenty-nine degrees, six minutes, twenty- 
five seconds And here you are to understand 

that a minute is the 6CUh part of a degree, and 
a second is the 60th part of a minute. 

E. Then, it is plain, that between change and 
change, the Moon goes 29 degrees, 6 minutes, 25 
seconds, more than round her orbit. 

iV. True, Eudosia ; and now I have only to tell 
j'ou farther, on this subject, that the Moon's going' 
round her orbit is called her periodical revolution j 
and that her going round from change to change^ 
is called her synodical revolution. 

£. I thank you, sir, for having told me so much. 
»...But are you not tired at present with hearing 
and answering my questions ? 



124 

. Very far from it I love these subjects. 

knd my talking with you about them, will keep me 
from forgetting them. 

E. Then I should be exceeding glad to know 
something about eclipses. 

2\ r . You shall know that very soon..... In Fig* 2. 
of PLATE V. let S be the Sun, M the moon, 
and E the Earth : a b c d the Moon's orbit, in 
which she moves according to the order of the 
letters j and C l b d D a part of the Earth's orbit, 

wherein it moves in the direction C D The 

Moon is new when she is at J/ a and full when 
she is at m* 

Draw the straight line A e E from the eastern 
edge of the Sun, close by the eastern edge of the 
Moon, to the Earth E : then draw the straight 
line B e E from the western edge of the Sun, 
close by the western edge of the Moon, to the 
Earth. 

Let these lines be supposed to turn round the 
middle line F ME; and the space e e, within 
them, between the Moon and the Earth, will in- 
clude the Moon's dark shadow, which is of a 
conical figure (like an inverted sugar-loaf), and 
covers only a small part of the Earth's surface at 
E : and only from that small part, the Sun will be 
quite hid by the Moon, and appear to be totally 
eclipsed : and it can be quits dark only at that 
part, because the Moon stops not the whole of the 
Sun's light at that instant of time, from any other 
part of the Earth It is evident, that if the Moon 



121 

were nearer the Earth, her dark shadow would 
cover a larger part of its surface ; and if she 
were farther from the Earth, her shadow would 
end in a point short of the Earth's surface ; and 
then she could not hide the whole body of the 
Sun from any part of the Earth : and those who 
were just under the point of the dark shadow,. 
w r ould see the edge of the Sun, like a fine lumi- 
nous ring, all around the dark body of the 
Moon. 

But although the Moon can hide the whole 
body of the Sun only from a small part of the 
Earth, at any time, when the Sun appears to be 
thus eclipsed by the moon ; yet, in all such eclip- 
ses, the Moon hides more or less of the Sun 
from a very large portion of the Earth's surface* 
For, 

Draw the straight line A f o from the eastern 
edge of the Sun, close by the western edge of the 

Moon, to the Earth at o Then draw the straight 

line Bfn from the western edge of the Sun, close 
by the eastern edge of the Moon, to the Earth at 
n* Let these lines ( Af 'o and Bfn) be supposed 
to turn round the middle line F ME, and their 
ends (n and o) will describe a large circle on the 
Earth's surface, around E ; within the whole of 
which circle, the Sun will appear to be more or 
less eclipsed by the Moon at M, as the places 
within that circle are more or less distant from its 
center E y where the dark shadow falls. For, 
when the Moon is at M, an observer on the Earth 

L 2 



126 

at », will see the western edge of ihe Moon, just 
as it were, touching the western edge of the San 
at B ; and an observer at o will see the western 
edge of the Moon, just, as it were, touching the 
eastern edgs of the Sun : but to all the places be- 
tween n and 0, the Moon will hide a part or the 
whole of the Sun, according as they lie between 
n and E, or between and E, or directly at -£.*... 
This faint shadow, all around the dark one, from 
n to 0, on the Earth's surface, is called the Penum- 
bra^ or partial shadow of the Moon. 

E. How many miles are contained in the di- 
ameter of the circle which the Penumbra fills, on 
the Earth's surface ? 

N* About 4709, when its center falls directlv in 
a right line from the Sun's center to the Earth's 

at a mean rate But when the Penumbra falls 

obliquely on the Earth's surface, its figure thereon 
will be elliptical; and then, the space that it 
covers will be much larger ; especially if the Moon 
be then at her least distance from the Earth. 

E. What! brother: is not the Moon's distance 
from the Earth always the same ? 

N. By no means : for the Moon's orbit is of an 
elliptical (or oval) figure ; and every ellipsis has 
two centers, which are between the middle and 
the ends of its longest diameter : and the Earth's 
center is in one of the centers (or, as they are 

called^ focusses) of the Moon's elliptical orbit 

So that, when I formerly told you, that the 
Moon's distance from the Earth's center is 



127 

240,000 miles, I only meant her mean (or middle) 
distance between her greatest and least distances. 

E. Then I understand that the Moon's distance 

from the Earth must be continually changing 

But supposing the Sun to be eclipsed when the 
Moon is at her least distance from the Earth; 
what is the diameter of the spot upon the Earth's 
surface that would be quite covered by the Moon's 
dark shadow ; from all parts of which spot, the 
Sun would be totally hid by the Moon ? 

j!?. About 180 miles. 

E. As the Moon's distance from the Earth is 
little more than a 296th part of the Sun's distance 
from it (as I have computed), I suppose the Moon's 
shadow at the Earth will move almost as fast as 

the Moon moves in her orbit Pray, in what 

time will the dark part of the shadow move over 
about 180 miles of the Earth's surface ? 

N. In four minutes and an half: and would go 
over that space sooner, if the Earth's motion round 
its axis (which is eastward, and consequently the 
same way that the Moon'o shadow goes over the 
Earth,) did not keep the place on which the sha- 
dow falls, longer in the shadow than it would be, 
if the Earth had no such motion. 

E* Then an eclipse of the Sun can never con- 
tinue total, above four minutes and an half, at any 
place of the Earth ? 

N. It never can, even when it falls on the Equa- 
tor, where the parts of the Earth's surface move 



128 

the quickest of all. And when it falls upon any 
part of Britain, whose motion is slower, because 
it is nearer the motionless pole, it would be soon- 
er over. 

E. How then could the sun be darkened so long 
as three hours, at the time of our SAVIOUR'S 
crucifixion, as it is mentioned to be in the Gos- 
pels ? 

JV. There is no way of accounting for that 
darkness upon astronomical principles ; for it was 
entirely out of the common course of nature. 

E. How do you prove that it was out of the 
common course of nature ? 

N- Because our Saviour was crucified on a full 
Moon day ; and then, the Moon being opposite 
to the Sun, could not possibly hide the Sun from 
any part of the Earth. 

E. I should be very glad to know how you 
can prove that the crucifixion was on a full Moon 
day. 

JV. Because it was the time of the Passover ; 
and the Passover was always kept at the time of 
full Moon. 

E. You have made this very clear And now 

if you please, I should be glad to have the cause 
of the Moon's eclipses explained. 

JV. In the same figure, draw the straight line A 
g c from the eastern edge of the Sun, close by the 
eastern edge of the Earth atgv and the straight 
line B h k from the western edge of the Sun, close 
by the western edge of the Earth at k — Let these 



129 

two lines be supposed to turn round the middle 
line F Mm, and they will include the space be- 
tween the part which is filled by the Earth's sha- 
dow g c k A.. ...It is plain, that, when the Moon is 
at m in her orbit, she is totally covered by the 
Earth's shadow, and eclipsed by it ; as it must 
then fall upon her, because the Earth is between 
her and the Sun. 

£. But how is it, that the Moon is at all visible, 
when the Earth must entirely stop the Sun's light 
from falling upon her, and she has no light of her 
own ? For, the same side of the Moon that is 
toward the Earth at her change, is also toward the 
Earth at her full. And, as we cannot see her at 
the change, I should think we could not see her 
when she is totally eclipsed ; because that side of 
her which is dark in the former case, when the Sun 
camfot shine upon it, should be as dark in the lat- 
ter, when the Earth intercepts the Sun's rays from 
it.. ••.But the Moon was very visible in her last to- 
tal eclipse : for I saw her, and she appeared of a 
colour somewhat like that of tarnished copper. 

-A 7 ". You are very shrewd in your remarks, sis- 
ter ; and I will tell, you why the Moon is not invi- 
sible when she is totally eclipsed. 

The air, or atmosphere, which surrounds the 
Earth, to the height of about 47 miles, is the 
cause of this. For, all the rays of the Sun's light 
which pass through the atmosphere, all around 
the Earth, in the boundary fg" h) of light and 
darkness, are, by the atmosphere bent inward^ 



130 

toward the middle of the Earth's shadow : and 
those rays, so mixed with the shadow, fall upon 
the Moon, and do enlighten her in some small 
degree. She reflects the rays back to the Earth 
which fall upon her, and so she is visible only on 
that account. For, if the Earth had no atmos- 
phere, its shadow w T ould be quite dark ; and the 
Moon would be as invisible, when she is totally 
immersed therein, as she is at the time of her 
change. 

E. I thank you, brother, for all these informa- 
tions ; but I still want more. 

N. Only say what they are ,• and I will inform 
you, if I can. 

-E. I see plainly by the figure, that the Sun can 
never be eclipsed (in a natural way) but at the 
time of New Moon ; because the Moon's shadow 
cannot fall upon the Earth at any other time ; 
and that the Moon can never be eclipsed but 
when she is full ; because that is the only time 
when the Earth's shadow can fall upon her. But 
though we have a new and a full Moon in every 
month of the year, I find my almanac mentions 
Lut very few eclipses ; and generally about half a 
year between the times of their happening. 

A 7 ". If the Moon's orbit a b c k d a lay exactly 
even (or in the same plane) with the Earth's orbit 
C b d D, as it is drawn on the flat paper, the Sun 
would be eclipsed at the time of every new Moon, 
and the Moon at the time of every full. But one 
half of the Moon's orbit lies on the North side oi 



131 

the plane of the Earth's orbit, and the other half on 
the South side of it : aad consequently, the Moon's 
orbit only crosses the Earth's orbit in two oppo- 
site points When either of these points are be- 
tween the Earth and the Sun, or nearly so, at the 
time of new or full Moon, the Sun or Moon will 
be eclipsed accordingly. But, at all other new 
Moons, the Mcon either passeth above or below 
the Sun, as seen from the Earth : and, at all other 
full Moons, the Moon either passeth above or 
below the Earth's, shadow. One of these points 
is called the Ascending Node of the Moon's orbit; 
because, when the Mcon has past by it, she as* 
cends northward, or to us, above the plane of the 
Earth's orbit: and the opposite point is called 
the Descending Node of the Moon's orbit ; be- 
cause as soon as she has past by it, she descends 
southward ; which, to us in the northern parts of 
the Earth, is below the plane of the Earth's or* 
bit. 

E. Supposing that either of these nodes were 
between the Earth and the Sun just now^ how 
much time would elapse before the other could 
be so ? 

N. It would be just half a year, if a line drawn 
from the one to the other kept always parallel to 
its present position (like the above-mentioned dia- 
meter of the Moon's orbit, k h, in Fig. 1.) : but 
the nodes move backward, or toward the West, 
contrary to the Moon's motion eastward in her 
orbit, at the rate of 19^ degrees efery year.. ...So 



132 

that^ from the time of the Sun's being in conjunc- 
tion with either of the Moon's nodes, to the time 
of his being in conjunction with the other, is on- 
ly 173 days, 7 hours, 3 minutes. 

E. As there must be so me distances from these 
nodes, within which the Sun and Moon must be 
eclipsed ; I should be glad to know what these 
distances are? 

JV. They are only 17 degrees for the Sun, and 
12 for the Moon. 

E. Now let me see : The Moon's whole orbit 
contains 360 degrees ; of which there are only 17 
on each side of each node, within which the Sua 
may be eclipsed. Twice 17 is 34, about one node, 
and there are as many about the other: in all 68 
degrees out of 360, for eclipses of the Sun. And, 
as there are 12 degrees on each side of each node, 
within which the Moon can be eclipsed, there 
must be no more than 48 degrees in all out of the 
whole 360, for the eclipses of the Moon. Am I 
right, brother ? If I am, it is no wonder that we 
should have so many new and full Moons 3 and so 
few eclipses. 

N. You are quite right, Eudosia ; and I am 
very glad to find that you make such a quick pro- 
gress. 

E. I know that the times of eclipses may be 
calculated before-hand, because I see they are al- 
ways predicted in the almanacks. Can you calcu- 
late them ? 

N. Yes. 



133 

E. I wish you would teach tne to do so too, if 
5'ou think I have a sufficient capacity for that 
branch of science. 

N. You have much more ; and I will instruct 
you with pleasure ; for you have not only learnt 
the four common rules of arithmetic, but even as 
far as the Rule of Three..... Aad in these calcula- 
tions, no farther arithmetic is necessary than ad- 
dition and substraction* But you must learn first 
to calculate the times of new and full Moons. 

E. That I will do, with very great pleasure. 

Nm Then we will set about it to-morrow morn- 
ing, if you please : but the whole will take up a 
week at least : during which time we must sus- 
pend our usual confabulations. 

E. I wish to-morrow were come alreadv. 

N. You remember the book which you saw, a 
few days ago, in this room ; in which you told me 
you had taken notice of something concerning 
the Ecliptic and its signs..... Did you look at the 
fritle-page of that book ? 

E. I remember the book very well ; but did 
not look at the title-page. 

iV. It is Ferguson's Astronomy. I sent for it on 
purpose to make you a present of it. There it 
is ; and I am sure you are qualified to read and 
understand it. 

E. I heartily thank you, dear Neander^ for this 
present. 

N. There are in it plain and easy tables and 
precepts for calculating the true times of new and 

M 



134 

full Moons and Eclipses. And, if you have any 
spare time to-day, I wish you would begin, by 
yourself, to read the precepts, and compare them 
with the tables, and with the examples of calcu- 
lation. And then if you find any thing difficult, 
mark it, and I will help you out to-morrow 
morning. Mean time if there be any thing else, 
which you would have us to talk about, before we 
are called to breakfast (which is later than usual 
to-day*) tell me what it is. 

E. I wish I understood the cause of the ebbing 
and flowing of the sea. But now the bell begins 
to ring for us. 

N. Very well»i...Be here in about an hour af- 
ter breakfast* 



Fim. B 



-%. /. 





«"6~— I 



: / 



Tie. 3. 



Ftyuttni del' 




Grav ATeiiJt. 




ttraus&ii del? 






DIALOGUE VIII 



ON THE CAUSE 0? THE EBBING AND FLOWING 

OF THE SEA. 



Neander. YOU are very punctual, sister....! 
have drawn out some figures for you since break- 
fast; and, just as you entered the room, I was 
putting the last letter of reference to them. Here 
they are. 

Eudosia. I thank you, brother ; and do sup- 
pose that, by these figures, you intend to explain 
the cause of the ebbing and flowing of the sea. 

N. I do. In Fig. 1. of PLATE VI. let A B 
C D A be the Earth, all covered with water, ex- 
cept the top of an island A a* Ivet the Eartl^ be 



IS<5 

In constant motion, turning eastward round its 
center is, every 24 hours, according to the order 
of the letters ABC D; and let 31 be the Moon, 
moving eastward in her orbit o, as from M to o 
in 24 hours, 50 minutes. You know that the 
Earth and Moon are within the reach of each 
other's attraction ; and therefore, as the Earth at- 
tracts the Moon, so the Moon re-attracts the Earth* 
E. Yes, Sir. 

N. Do you remember my telling you, some days 
ago, that the attraction diminishes, as the square 
of the distance from the attracting body increases? 
E. I remember it very well, 
N. Then you know, that the Moon must at- 
tract the side A of the Earth which is nearest to 
her (at any time) with a greater degree of force 
than she attracts the Earth's center E ; and that 
she attracts the center E with a greater degree of 
force than she attracts the side C of the Earth, 
which is then farthest from her. 
E. Certainly. 

N. And that the Earth and Moon would fall to- 
wards one another, by the power of their mutual 
attractions, if there was nothing to hinder them : 
and that the Moon would fall as much faster to- 
ward the Earth than the Earth would fall toward 
the Moon, as the quantity of matter in the Earth 
is greater than the quantity of matter in the 
Moon. 

E. Undoubtedly so ; because every particle of 
matter attracts with an equal degree of force ; am- 



137 

therefore, the body which has the greater quanti- 
ty of matter must attract the other with so much 
the greater degree of force. 

iV*. Well done, Eudosia. Let us now suppose 
the Earth and Moon falling toward each other* 
The earthy parts of our globe being connected, 
and cohering together, would not yield to any 
difference of the Moon's attractive force ; but 
would all move equally fast toward the Moon : as 
if a cord were tied to each end of a great folio 
book on the table, and you should pull one cord 
with the force of four pounds, and I pull the other 
cord the same way with the force of eight pounds* 
so as to move the book ; all the parts of it will 
move equally fast, notwithstanding the different 
forces by which you and I pull it* But the wa- 
ters are of a yielding nature ; the coherence of 
their particles being very small, and therefore^ 
they will be differently affected, according to the 
different degrees of the Moon ? s attractive force? 
at different distances from her* 

And therefore, as the waters at A are more at- 
tracted by the Moon than the Earth is at its center 
J?, they move faster toward the Moon than the 
Earth's center does ; and consequently, with res- 
pect to the Earth's center, they rise higher toward 
the Moon, as from A to a : and as the center E 
moves faster toward the Moon than the waters. on. 
its surface at C do ; the waters at C will be, as it 
were left behind, and consequently, with respect 
to the center E y they will be raised, as from Q to c» 

at 2 



138 

E. So far, I understand you perfectly well. 

N. But as there is still the same quantity of wa- 
ter on the whole Earth, the waters cannot rise at 
one place without falling at another—And there- 
fore, the waters must fall as low at b and d as they 
rise, at the same time, at a and c: so that an ob- 
server placed over E y at a distance from the Earthy 
would see the surface of the waters not of the 
round shape A B C D, as they would be if the 
Moon did not disturb them by her attraction, but 
of the elliptical shape abed* 

Then, as the Earth turns eastward round its 
axis, it is plain, that when the island A a is at A, 
it will be in the high zvater, under the Moon Mi 
when it is at B, it will be in the low water^ six 
hours from under the Moon : when it is at C, it 
will be in the high water again, twelve hours from 
under the Moon : ioid when it is at Z), eighteen 
hours from being last under the Moon, it will be 
in the low water again. So that, if the Moon 
had no progressive motion in her orbit o, but 
kept always in the same right line A M, the island 
A a would have two ebbings and two flowings of 
the sea every 24 hours. 

E* It would. But I find the tides are put down, 
m my almanac, later every day than on the day 
before. And now, I apprehend the reason of this 
to be, that as the Moon goes eastward round her 
orbit in a month, and the Earth turns eastward 
round its axis, every 24 hours ; the Moon make? 



139 

part of a revolution in the time that the Earth 
makes a whole rotation : and therefore, the Earth 
must turn as much more than round its axis, be- 
fore the same Island can come even with the 
Moon again, as the Moon has advanced in her 
orbit during that interval of time. 

N. You are right, Eudosia : for, in the g time of 
the island's revolving from- A to A again (in the 
direction A B C D A)> which is 24 hours ; the 
Moon moves from M almost to o in her orbit ;: 
and therefore, after, the island has come round to 
A again it must move on from A to e*, before it 
can be in the middle of the tide of flood the next 
day, under the Moon,, which, will have then 
moved from A to a. 

E. How long is the island- in moving from A. 
toef 

N. Full 50 minutes : and so much later are the 
tides every day than they were on the day before, 
The sailors call it only 48 minutes ; and it would 
be exactly so, if the Moon were 30 complete day?, 
and nights going round from change to change. 
But as the time is only 29 days, 12 hours, 44 
minutes, 3 seconds, (at a mean rate) she must 
.move a little farther every day than she would if 
she took the full 30 days: and this difference is 
equal to about 2. minutes of time, of the Earth's 
motion on its axis . 

E. Then as "the Moon goes round her orbit, 
from change to change, in 29~ days (in round 
nujnbers), the island A a can only come 28| times 



140 

round from the Moon to the Moon again, in that 
time ; and consequently, it can have no more 
than twice that number of tides of flood, at a and 
c; or 57 tides of flood and as many of ebb, be- 
tween change and change of the Moon. 

N. You are very right : and consequently, in 
two courses of the Moon, from change to changer 
which is 59 days, 1 hour, 28 minutes, 6 seconds, 
there are only 57 double tides of flood r and, as 
manv of ebb. 

E. This account of the tides would be extreme- 
ly natural, and easy to be understood, if the Earth 
and Moon were continually falling toward one 
another. But seeing that the Moon's motion in 
her orbit gives her a centrifugal force r equal to the 
force with which the Earth attracts her, she can- 
not fall toward the Earth at all. And, from 
what you told me, in our second dialogue, about 
the Earth and the Sun, I should think, that if the 
Earth itself did not describe a small orbit round 
the common center of gravity between it and the 
Moon, in the time the Moon goes round her or- 
bit, the Moon's attraction would take the Earth 
away, as it would have no centrifugal force to 
balance her attraction. 

N* Dear sister, you cannot imagine how much 
pleasure it gives me to talk with you on these sub- 
jects ; on account of the proper inferences and 
applications you make — The Earth and Mooon 
do really move round the common center of gra- 
vity between them, every month ; and it is that 



m 

center of gravity that describes the very orbit in 
which the Earth's center would move round the 
Sun in a year, if the Earth had no Moon to at- 
tend it. 

E. You may thank yourself, Neander y for all 
those inferences and applications ; as they only re- 
sult from your explanations, and leading me so 
gradually on, from one subject to another. But, 
pray, how many miles is it from the Earth's center 
to the common center of gravity between the Earth 
and Moon? Undoubtedly that distance compared 
with the Moon's distance from the Earth's center 5 
must be in proportion to the quantity of matter in 
the Moon compared with the quantity of matter 
in the Earth. If you will tell me how much great- 
er the quantity of matter in the Earth is, than the 
quantity of matter in the Moon, I will try to com- 
pute how far the common center of gravity be- 
tween them is from the Earth's center.. 

£. Very well.. ...And the Moon's mean dis- 
tance from the Earth's center is 240,000 miles.. 
Now, I divide 240,000 by 40, and the quotient is 
6000 ; which, I think must be the common center 
of gravity between the Earth and the Moon ? 
from the Earth's center : and that the said com- 
mon center of gravity must always be in a right 
line between the centers of the Earth and Moon; 
because both these bodies move round it. Am I 
right, brother ? 

N* Indeed you are ; and before we talk further 
about the common center of gravity between the 



*4S 

Earth and the Moon, I will endeavour to illus- 
trate this affair about the tides to you, in a differ- 
ent manner from what I have done. For I find* 

at even if I had intended to explain it by the 
falling of the Earth and Moon toward each other, 
you would have justly believed that I was mis- 
leading you. 

Here is a circular hoop {Fig. 2.) A B C Z), of 
thin plate brass. You see it is very flexible : for 
as I pull out the parts A and C to a and c, the 
parts B and D fall in to b and d; and the hoop 
becomes of the elliptical shape abed. 

E, True ;... .and just like the shape of the sur- 
face a b c d of the water (in Fig. l.J,as affected 
by the Moon's attraction. 

X. But, if I quit my hold of the hoop at a and c, 
it will return to its former circular shape ABC D* 

E+ I see it does, now you have left it at liberty. 

N. And if the Moon's attraction should cease 
(Fig'. 1. )the waters a b c d would return, from their 
elliptical shape a b c d, to their former round sha 
A B C D. 

jE\ Yes ; for they would run from the highest 
parts a and c to the lowest parts b and d, till their 
surface was equally distant from the Earth's center 
jE, all around. 

N. Now I tie the end A (Fig. 2.) of the string 
A H lo any part, as A of the circular hoop A B C 
D, and take hold of the other end H of the string 
with my hand. If I whirl the hoop round 
head like a sling, what do you think will happen- 



14 



JE". Why ; the hoop will endeavour to fly off, as 
a pebble in a sling would do. , 

N. True : but do you think that all the parts of 
the hoop will then have an equal tendency to fly off? 

E. Let me consider,. .J think they will not* 
For, as the part C will go round your head in the 
same time as the part A, but faster, because it is 
further distant from your hand ; I imagine that 
the part C will have as much more tendency to fly 
off than the part A has, as its distance from your 
hand is greater. 

N. Exactly so, because it will move so muci\ 
faster, as the circle it describes is larger. Now 
observe, I^whirl it round my head. What shape 
is it noxo of? 

E. It is of the elliptical shape a be d. 

N. Yes, for the tightness of the string draws out 
the side next my hand, A to a ; and the centrifu- 
gal force of the other side throws it out as far 
from C to c. And now, if an inflexible circular 
ring (like the rigid Earth) A B C D should lie 
upon the elliptical hoop a b cd y and turn 29 times 
and an half round the center is, in the time 
the hoop and circle were moved once round my 
head ; would not any point, as A, of the circular 
ring, come successively even with the highest parts 
a and c of the elliptical hoop, and with the lowest 
parts b and d of it: as the island A a (Fig. 1.) 
comes to the high water at a and b, and the low 
water at c and d 7 by the Earth's motion on its axis ? 



144 

jE* It would. And I think that Fig'. S. is some- 
what analogous to Fig* % 

N* It is very much so ,* and now is the proper 
time to explain Fig. 3. 

Let AB CD be the Earth, M the moon, e 
part of the moon's orbit, and G the common cen- 
ter of gravity "between the Earth and the Moon, 
round which both these bodies move, once a 
month ; the Moon in the direction O #, and the 
Earth in the direction E h. By this motion all 
the parts of the Earth will have a centrifugal force 
or tendency to fly off in or parallel to the line A 
EC : and the centrifugal force of each part will 
be directly in proportion to its distance from the 
common center of gravity G ; because the spaces 
through which these parts move, will be respec- 
tively as their distance from G ; that is, as the 
semi-diameters of those circles which they all de- 
scribe in the same period of time. Thus, the cen- 
trifugal force of the point A will be as the line A 
G ; the centrifugal force of the center E will be 
as the line EG; and the centrifugal force of the 
point C will be as the line C G ; for the point A de- 
scribes the small circle A efg A in the time the 
point E describes the larger circle E h i k E, and 
in the time the point C describes the still larger 
circle C Imn C ; which is in a month ; and in 
that time, the Moon goes round her orbit a* 

The Moon's attraction at the Earth's center E 
exactly balances the Earth's centrifugal force at 
E ; and consequently retains the center E in the 



145 

iDrbit E hi k E. But her attraction at A is greater 
than at E, and less at C than at E. So that where 
the Moon's attraction is greatest, as at A, the cen- 
trifugal force is least ; and therefore, the excess 
of attraction causeth the waters to rise, as from A 
to a, on the side of the Earth which is at any 
time nearest the moon M* But at C (the side 
which is then farthest from the Moon) the attrac- 
tion is least, and the centrifugal farce greatest: 
and therefore, the waters will rise as high from 
C to c, by the excess of the centrifugal force 
there, as they rise on the opposite side from A to 
a by the excess of the Moon's attraction. Are 
you satisfied now, Eudosia ? 

E. I was sadly afraid, that the rising of the 
tides on the side of the Earth which (at any 
time, by its motion on its axis) is turned away 
from the Moon, would be very difficult to account 
for. But y<m have made it just as plain, that they 
must rise as high on the side of the Earth which 
is opposite to the Moon, as they do on the side 
which is under the Moon. Did you ever see this 
confirmed by any experiment ? 

N. Yes ; I have seen Mr. Ferguson do it, to the 
satisfaction of every observer, by a plain experi- 
ment in one of his machines, called the Whirling 
Table ; and he is the first that ever did so. He 
has given a full account of it in his Lectures on 
Mechanics, Hydrostatics, Pneumatics, Optics, with 
the Use of the Globes, and the Art of Dialing* In 
that book, there are plates of all his machines for 

N 



t4o 

. I shall send for it to-morrow - 
and makr you a present of it, on account of the 

ve made in astronomy: and 

elf, learn a course of ex- 

I philosophy* 

E. Indeed, brothr n lay me under so many 

obligations, that I shall never be able to make you 

eturn for them. But there is one 

.t I had almost forgot to ask you. Pray, 

is meant by the Spring and Neap Tides? 

K. The Earth is so small, in comparison of its 

:m the Sun, that the Sun's attractive 

ce is nearly equal on all parts of the Earth: 

1 therefc ::. there can be but little difference 

en the centrifugal force on the side of it 

the Sun, and the centrifugal force 

the opp : = ::e side- But still there is some dif- 

the E:.:;h mores on in its orbit. And 

therefore if the Earth had no Moon to attend it, 

uld be small tides occasioned by the Sun. 

Consequent! Sun. Mean and Earth? 

^ht line (which they are at the time 

new and full Moon) their joint actions 

rj and so raise the tid^ higher at these 

times than at a»y other i and those are called the 

Spring Tides. But, wher ire Mc... 

quarters, he ion on the tides is cross- wise to 

the Sun's ; : e Sun is in a line with the 

low water, and his action keeps the 

falling so low there, and consequently from rising 

bo high under and opposite to the Moon, as 



147 

would do by the action of the Moon, if the Sun 
did not disturb them at all ; and these are called 
the Neap Tides. 

E. I understand you very well; and do see 
plainly, that a straight line drawn from the Moon's 
center through the Earth's center, would he in the 
highest part of the tides on both sides of the 
Earth. 

N. You are a little mistaken in that point, Eu- 
dosia ; which may be owing to its being so repre- 
sented in the figures. But, I am sure, you would 
not have been so, if you had remembered what I 
told you in our first dialogue ; namely, that all 
bodies which are put into a state of motion will 
persevere in that motion, till something stops their 
course. If you put water into a bason, and give 
it a little shake, and then settle the bason sudden- 
ly, the water will rise a little further, on the side 
to which you gave it the motion, after the bason 
is settled again, than it did in the instant when 
you settled it. Pray, have you forgot your fall in 
the boat, when it struck against the bank of the 
river ? 

E. I have not, brother; and the inference i.s 
plain. 

N. It is : and therefore you know, that when the 
waters are put into a rising state of motion by the 
action of the Moon ; they would rise a little high- 
er if the Moon were annihilated at the instant of 
her being on the meridian, even of a place where 
she was directly over head. But you are still to 



148 

:sider fa: although the M :: 

nat anyplace is greatest when she i 
meridian of 1 

i>t that she can be to the place on that d: 
yet her attraction at th ce dots not then cease, 

hut for some time ai the 

Meridian; and this continuance of traction, tho* 
weaker, will cause the waters to keep on in their 
r :ate, till the attr just balances the 

of the waters to fa gain* 

L* I thank you, brother, for setting me right. 
But, pray, how long is the Moon past the meri- 
n when the water is at the highest. 
K. If the Earth was covered all orer with wai- 
ter, so :.: the two eminences of the tides at a and 
c might regularly follow the Moon ; she wo did a2- 
th r e e h . , e meridian of any g i v e o 

:e> when the tide was at the highest as that 
:e. Bat as th .rth. is not all covered with 
water, and the different capes and cor: of the 
land run out all manner of ways into the cce:. 
and seas ; the regular course of the tides is mu 
interrupted thereby; and also by their runni 
through shoals and channels* So that, at differ 
tes, the tides are highest at ve afferent d 

he Moon from the meridian. But at 
:e the Tvloon is from the mel- 
on at any pla * n the tide is at 
its height there, i be so oe next day, 

be time when the moon is at the 1: 
distance from the meridian again. 



149 

E. You have quite satisfied me about the tides ; 
and now I will go to my room and study Fergu- 
son's Method of calculating the Times of New 
and FuH Moons. 



2'n 



150 



DIALOGUE IX, 



ON TliE FIXED STARS, AND SOLAR AND SYDEREAL 

TIME. 



:o: 



Neandcr. WHAT is the matter, sister? Sure- 
ly you could not have gone to your room and re- 
turned, since you left me. 

Endosia. I had scarce gone out of this room* 
v/hen something came into my mind, which was, 
that you promised me, some days ago, to demon- 
strate that all the stars are at resU...,And lest I 
should forget it again, I now beg leave to remind 
you of it, if you have leisure at present. 

N. For that, I refer you to Ferguson's Astro- 
nomy: and, before you have read the first three 
chapters you will not only be convinced that all 
the Stars are at rest, but also that they are Suns 
to innumerable systems of planetary worlds, as 
our Sun is to its own system of planets* 



151 

E. What ! other Suns, and planetary worlds 
belonging to them ! You amaze me ! 

Nm The Deity is infinite in all his perfections ; 
and as he has power enough to create and place 
Suns and AVorlds throughout the whole infinitude 
of space, so he has goodness enough to induce him 
to do it. But now, if you please, I will tell you 
of something which I did not think of before y 
namely, to inform you of the difference between 
Solar and Sydtreal Time. 

E. You speak too learnedly for me just now, 
brother ; and it is the first time you ever did so. 

N. Solar time is the time measured by the 
Sun's apparent motion round the Earth ; and sy- 
dereal time is the time measured by the Stars in 
their apparent motion round it. 

E. Now I understand you i and have often ob- 
served, that if any Star be seen, just as if it were 
oyer a neighbouring chimney, at any hour in the 
night ; in a week afterward, the same Star is soon- 
er seen over the same chimney. 

JV. True : and in 365 days, the stars seem to 
have made 366 revolutions about the Earth; so 
that they gain one hour every 24th part of the year 
upon the time shewn by a well-regulated clock. 
And therefore, every Star comes almost four 
minutes sooner to the meridian, every succeeding 
day or night, than it did on the day or night be- 
fore. The real difference is 3 minutes, 55 seconds, 
and 54 sixtieth-parts of a second. So that, if one 
clock should be so well regulated as to shew the 



252 

time to be XII at noon this day, and on the 365th 
day afterward ; and another clock should be so 
regulated as to shew the time to be XII every day 
or night when any given Star is on the meridian ; 
the latter clock would gain 3 minutes, 55 seconds, 
and 54 sixtieth-parts of a second upon the former, 
in each revolution of the same Star to the meridian. 
JS. What is the reason of this ? 
N. Much the same as that of the Moon's going 
round her orbit in less time than she goes round 
from change to change, or from between the Earth 
and the Sun to the same position again : as I ex- 
plained to you, by Figure 1. of PLATE V. last 
Monday morning, in our Seventh Dialogue : and 
we may make the same figure do for the present 
subject. You rememeber I told you that the whole 
diameter of the Earth's orbit is but as a point, in 
comparison to the distance of the Stars ; which is 
the same as to say, that a globe of 190 millions of 
miles in diameter, which would fill the Earth's 
orbit, would appear no bigger than a dimension- 
less point, if it were seen from any of the Stars : 
and the present subject will prove this to be true* 
E. lam far from doubting the truth of your 
word ; but I should be very glad to sec the de- 
monstration. 

N. Then, here it is. Let the Earth be in what 
part of its orbit it will, we always find the interval 
of time (by the best clocks that are made) between 
any Star's revolving from the mu idian to the me* 
ridian again, to be equal throughout the whole 



153 

year : which it could not be, if the Earth's change* 
ing its place, by a whole diameter of its orbit, 
bore any sensible proportion to the distance of the 
stars. For then, if the hour and minute hands of 
a clock should revolve exactly 366 times from XII 
to XII again (there being supposed to be 24 hours 
on the dial-plate) in the time of the Star's making 
366 revolutions from the meridian to the meridian, 
again ; and the hands be set to the uppermost XII> 
when any given Star is on the meridian on the 21st 
of December ; then, on the 20th of March after- 
ward, when the hands were at the same XII as 
before, the same Star would be a little on the east 
side of the meridian, if the Earth's orbit were of 
any sensible bigness in proportion to the distance 
of the Star ; and a little on the v/est side of the 
meridian, when the hands were at XII on the 23d 
of September : but we never find any such differ- 
ence. 

E. To me, your demonstration is self-evident. 

N. Then, you are convinced, that when the me- 
ridian of any place has revolved from any Star to 
the same Star again, the Earth has turned abso- 
lutely once round its axis; because the same me- 
ridian lhas revolved so, as to be again parallel to 
any fixed plane, to which it was parallel before, 
when the same Star was upon it. 

E. I am. 

JS T . Very well, sister Now, in Figure 1. of 

PLATE V. let *Sbe the Sun, A B C D E F G one. 
half of the Earth's orbit ; let the circle h i k Ik be 



154 

the Earth at the top of the figure, and a h the 
meridian of London, which we shall suppose to 
be at h. 

Let the straight line a h S be produced onward, 
to five or six miles beyond the Sun S y as seen from 
h ; and let a Star be placed at the farthermost end 
of that line. •..Then, the distance of the Star from 
the Sun will be so great, that the Earth's orbit A 
B Cf Sec. will bear no sensible proportion thereto, 
if it were viewed from the Star ; and therefore, to 
an observer on the Earth at /*, the Star will appear 
as e\en with the line d h, when the Earth has got 
a quarter round its orbit from a to d, and the me- 
ridian d h parallel to the position it had at a h> as 
when the Earth was at a in its orbit: so that, let 
the Earth be in what part of its orbit it will, the 
Star will always be upon the meridian of the place 
A, when that meridian has revolved to the same 
parallel position again : which it will always do in 
the time of the Earth's turning absolutely round 
its axis. 

E. Undoubtedlv it will. 

jV. Now, suppose the Earth to advance in its 
orbit from a to 6, in the time that it turns once 
round its axis ; and then, the same meridian b h 
will be parallel to the position it had at a h, when 
the Sun and Star were both even with it ; or, as 
we say, upon it. 

Then it is plain, that when the Earth is at b, and 
the meridian b h has revolved from the Star to the 
Star again, it must revolve further on, from b to? 5 ; 



before it can go round from the Sun to the Sun 
again at J. And the arc, or part h m, of the Earth's 
circumference bears the same proportion to the 
Earth's whole circumference, that the arc, orpait 
a b of the circumference of the Earth's orbit bears 
to its whole circumference. 

When the Earth is at c in its orbit, and the 
same meridian c h comes even with the Star the 
second time, the meridian must revolve from h 
to n before it can be even with the Sun again, or 
the Sun be upon it the second time. 

When the Earth is at d, a quarter round its or- 
bit from «, and the meridian d h is even with the 
Star ; the meridian will w r ant six hours of being 
even with the Sun in the right line d o S, and the 
place h must revolve six hours, or through the 
arc h o of 90 degrees, before the Sun can be on 
its meridian d h. 

And consequently, when the Earth has gone 
half round its orbit, the same meridian will be 
even with the Star 12 hours before it revolves to 
the Sun : and when the Earth has gone three 
quarters round its orbit, the meridian will be even 
with the Star 18 hours before it comes to be even 
with the Sun. 

And lastly, when the Earth has gone quite 
round its orbit, its rotation on its axis will have 
brought the same meridian once more round from 
the Star to the Star again, than from the Sun to 
the Sun again. So that, let the year contain how 
many days it will, as measured by the apparent 



156 

revolutions of the Sun from the meridian to fchfc 
meridian again, it will contain one day more, as 
measured by the apparent revolutions of the Stars. 

E. By this I find, that one absolute turn of the 
Earth round its axis is lost in a year with respect 
to the number of solar days in the year, because 
the Earth's motion on its axis is the same way as 
its motion round the Sun. For, to bring any me- 
ridian round from the Sun to the Sun again, the 
Earth must turn as much more than quite round 
its axis, as bears a proportion to the space it moves 
in its orbit in 24 solar hours. And therefore, to 
make the year contain 365 solar days and nights* 
the Earth must turn 366 times round its axis. 

JV. You are right, Eudosia.»...Now go to your 
astronomical tables and precepts ; and try whether 
you can calculate the time of new Moon in July 
1748 old style.. ..If you find any difficulty, come 
and tell me of it. 

E. I thank you, brother ; and make no doubt 
but that I must soon see you again. 



ur 



DIALOGUE X, 



-ON THE PROJECTION OF SOLAR ECLIPSES ; TO 
WHICH, ANSWERS TO SOME ASTRONOMICAL 
QUESTIONS ARE SUBJOINED, 



:o: 



Neander. WELL, sister ;.... you kept quite alone, 
all the time yesterday after you left me : and as 
you did not return this morning before breakfast) 
as usual, I sent to enquire about your health ; and 
the maid told me that you was very well ; but so 
much engaged with your book and pen, that she 
was almost afraid to speak, for fear of disturbing 
you, as you took no notice of her when she came 
into your room. 

Eudosia* Indeed, brother, I have been very 
much engaged; and scarce took time to eat either 
dinner or supper. 

o 



I5g 

JNl So I observed ; and now, pray, what have 
you been doing ? 

E. After looking a little at Ferguson* s tables for 
calculating the true times of new and full Moons, 
and finding some expressions in the titles of the 
tables which I did not understand, namely* the 
mean Anomalies of the Sun and Moon ; I read 
the former part of the 19th chapter of his book, 
in which I not only found these terms explained to 
my satisfaction ; but also the principles on which 
the tables are constructed : and, on account of 
what you have already told me about the attrac- 
tions of the Sun, Moon> and Earth, I think I un- 
derstand the principles tolerably well. 

JV 7 . I can very easily take your word for that, 
£udosia* 

E. Having read the Precepts, and compared 
them with the tables and examples of calculation, 
I then tried to calculate the true times of some 
new and full Moons which are exemplified in 
the precepts ; and finding my calculations to agree 
very nearly with Fergusotfs examples, I tried to 
calculate the true time of the new Moon in July 
1748, old style, as you desired me; of which 
Mr. Ferguson has given no example And find- 
ing that the Sun must have been eclipsed at the 
time of that new moon, I even attempted to take 
out the elements for projecting that eclipse. 

JV. Then indeed, you must have done a great 
deal of work for the time you have been about it» 
Pray, show me your calculations. 



159 , 

£. I am almost afraid to do it; but, here they 

are. 

1. The apparent time of new Moon at clay h. m. s. 
Greenwich, July in the Forenoon 14 11 15 3 

2. The semi-diameter of the Earth's disc ° ' " 
at that time, as seen from the Moon 53 32 

3. The angle of the Moon's visible path 

with the ecliptic - - - 5 35 

4. The Moon's latitude North descending 28 6 

5. The Moon's horary motion from the Sun 27 17 

6. The Sun's distance from the nearest sol- 
stice ..... 32 42 40 

7. The Sun's declination, North - 19 35 21 

8. The Sun's distance at noon from the 

vertex of London - - - 31 54 39 

9. The Sun's semi-diameter - - 1 5 50 

10. The Moon's semi-diameter - 14 53 

1 1, The semi-diameter of the Penumbra 30 43 

JV. Well done, Etidosia. I calculated the same 
elements before I gave you the book ; and now 

we will compare the calculations together Ail 

right; for do you see...... we hav not differed 

three seconds in any part. And I did not tell 
you till now, that I had made any such calculation. 

E. This gives me great pleasure, indeed But ? 

upon reading the method of projecting eclipses, I 
often find mention made of a Sector-, which I 
take to be a mathematical instrument ; and, as 
you know that I am entirely unacquainted with 
any of these instruments, I am afraid I can pro- 
ceed no farther, unless you will show me a Sector, 
and teach me how to use it. 



160 

i\T. It is true, that by means of a Sector, these 
kinds of projection may be much sooner made 
than without it. But as I know you are yet totally 
unacquainted with mathematical instruments, I 
will now shew you how to project an eclipse of the 
Sun, only by means of a pair of compasses and a 
common ruler : And then, you will be at no loss 
about projecting any eclipse of the Moon ; which 
is much easier to be done than to project an eclipse 
of the Sun. I will first tell you some things, by 
which you will understand the reason why all the 
different parts of the construction of a solar eclipse 
must be as we lay them down; and then proceed 
to construct the Sun's eclipse which fell on the 
14th of July 1748, as it appeared at London. You 
know, it is but a few days since you covered one 
of the panes of glass in the window of your room 
with gum water ; and, when it was dry, you placed 
yourself about a foot from the glass, and keeping 
your head steady, you delineated a landscape on 
the glass, with your black lead -pencil* of all the 
distant objects- which you saw through the glass, 
drawing them on those parts of the glass which 
were just between them and your eyes ; as if the 
pencil had touched the objects themselves. 

E. I have often done so : then drawn them with 
ink (which the gum-water causes to stick), and 
then laid a paper over them on the glass, and 
traced them thereon with the black-lead pencil. 

N. Now, suppose the Equator to be a visible 
circle on the Earth, and that a circle is drawn 



161 

through any place (as suppose London) parallel 
to the Equator : that the Earth had an axis put 
through it, projecting out a good way from its 
surface at each pole ? and that there was a visible 
line drawn perpendicular to the plane of the eclip- 
tic or Earth's orbit, which line would be called 
the axis of the ecliptic. 

Imagine all these things would be visible to an 
observer at the Sun ; and suppose yourself to be 
there, holding a pane of glass between you and die 
Earth, and delineating the figure of the Earth 
thereon with its axis, Equator, the circle parallel 
to the Equator passing through London, and the 
axis of the ecliptic. Then, 

As the Earth turns round its axis from west to 
east, the places on its surface would appear to you 
to move as from your left hand toward your right ; 
and you would see London as moving over the 
Earth in the circle which is drawn through it, pa- 
rallel to the Equator. And, when the Moon is new, 
and eclipseth the Sun from any part of the Earth, 
you would see her between you and the Earth, as 
passing over it from left to right hand, the same 
way as it turns on its axis : and you would see a 
great part of the Moon's penumbra or partial 
shadow, all around her (as it were) like a dark 
brownish ring, travelling with her over the Earth. 
As the Sun shines round the north pole of the 
Earth, from the 20th of March to the 23d of Sep« 
tember, you would see that pole all the while m 
the enlightened part of the Earth's disc (or flat 

o 2 



162 

round surface, as it would appear to you ; like as 
the Sun and Moon do to us :) and, from the 2od of 
September to the 20th of March, the same pole ' 
would be hid from your eye-sight behind the 
visible and illuminated disc of the Earth ; because 
it is in the dark all that time. 

If a straight walking-stick be placed at a dis- 
tance from you, and inclining either directly to- 
ward you or from you, it will appear to you to be 
upright: but, if it inclines either toward your 
right or left hand, you will perceive it to do so. 
Therefo e, when the Earth's axis inclines either 
directly toward you or from you at thfc Sun, it will 
appear to you to be perpendicular to the plane of 
the Earth's orbit or ecliptic ; and to coincide with 
the axis of that plane* But when the Earth's axis 
inclines more or less sidewise to the Sun, the north- 
ern half of it will appear to you to incline from 
the axis of the ecliptic toward your right or left 
hand ; and the southern half to incline the con- 
trary way from the axis of the ecliptic : for then, 
these two axes will seem to cross each other in 
the middle point of the Earth's axis. 

Now, as the Earth's axis really inclines 23§ de- 
grees from a perpendicular to the plane of the 
Earth's orbit, and always keeps inclining to one 
and the same side of the heavens, in the Earth's 
whole course round the Sun ; it will appear in 
different positions of inclination to the axis of the 
ecliptic, as seen from the Sun, at different times 
of the year 5 the north pole being sometimes to- 



^■••1v% 



#S 







"B 



CO 






163 

ward your right hand from the axis of the ecliptic f 
and at other times toward your left hand from 
the axis of the ecliptic ; constantly varying the 
apparent angles of its inclination, according to 
the time of the year. 

From the 21st of December to the 2 1 'st of June, 
the north pole of the Earth's axis lies toward the 
right hand from the axis of the ecliptic, as seen 
from the Sun ; and most of all so on the 20th ot 
March. From the 21st of June to the 21st of 
December, the north pole of the Earth's axis lies 
more or less to the left hand, as seen from the 
Sun ; and most of all so on the 23d of" September.. 

E. I wish you would be so good as to write 
down these matters for me when you are at lei- 
sure ; because I am afraid I shall forget them. 

N* You may depend upon it that I will ; espe- 
cially as they are the very principles on which we 
are now about to construct an eclipse of the Sun: 
which is, in the first place, by delineating a figure 
of the Earth, with its axis, Equator, £s?c. according 
to their positions, as supposed to be seen from the. 
Sun Tor from the Moon just between the Earth and 
the Sun) at the time of the eclipse. Now we will 
go to work, according to your calculated elements. 

Make a scale, as y A t? (PLATE VII. Fig. 1.) 
almost half the length of the paper intended for 
your projection, and divide it into 60 equal parts 
at least, reckoning each part to be one minute, or 
a sixtieth part of a degree... .Then, take the semi- 
diameter of the Earth's disc, 53 minutes, 32 se- 



n.vn 



ATrty'eclion of the Sum T, dips e observed 
aKtohdon, July i /'.!< if 48. Md JUtt. 



o IS .30 




It 

c on d s (or 5 3 1-, ) fro m th e s i o y o u r c o m 

I with that extent, set one foot in the end C 
scale as a centre ; and with the other foot dies- 
bribe the semicircle, AD B for the circumfcrer. 
f the northern half of the Earth's ilium inat 
: or surface, because v r e on the north side 
of the Equator: and continue the linr I C on 
I) ; so A C B shall be a portion of the Eclip: 
al to the diameter of the Earth as from 

Sun or Moon at that time. 
From the center C, raise the line C D Z7, per- 
pendicular to A C B ; and call the line C D H the 
s of the ecliptic. 

Divide the quadrants A D and D B each into 90 

I parts for degrees, beginning at D. Then 

connect the points E and G (which are 23| de- 

ide of Z)) with the s: ht line 
FG; in h line, the North pole P of the 

Earth's disc will always be found. 

Set one foot ot the comp: in the point F, 

•where the line E F G intersects the axis of I 
C D H ' , and, having tided the ot' 

prom F to £, or from Fto G, describe the se- 
micircle E H G, and divide its quadrant HE into 
90 equal ps for degrees, because the Earth's 
axis lies to the left hand from the axis of the ec 
tic, as seen from the Sun in the month of July.., - 
If the Earth's axis had lain to the right hand from 
the axis of the ecliptic, the quadrant H G n: 
have been divided into 90 de :.nd not the 

/.adrant H E> 



165 

As the Sun is 32 degrees, 42 minuses, 40 se- 
conds, (which may be estimated 32 degrees and 
four-sixths, or two- thirds, of a degree) from the 
nearest (or summer) solstice, which is the first 
point of Cancer, on the noon of the 14th of July 
1748, draw the right line / P, paralled to H D, 
from 32§ degrees of the quadrant H E, till it meets 
the line E/Gat P: then from P to C?, draw the 
right line P C ; so P C shall be the Northern half 
of the Earth's axis, and Pthe North pole 

As the Sun is on the North side of the Equator 
in July, and consequently nearer the point of the 
heaven just over London (or the vertex of Lon- 
don) that the Equator is ; substract his declination, 
19 degrees, 35 minutes (neglecting the 21 seconds) 
from the Latitude of London, 51 degrees, 30 mi- 
nutes, and the remainder will be 31 degrees, 55 
minutes, for the Sim's distance frGm the vertex 
of London on the noon of July 14th. 

From the point k (in the right hand side of the 
semicircle A D B) at 31 degrees, 55 minutes, 
counted upward from B, draw the right line k /, 
parallel to C D : and taking the extent k I in your 
compasses, set it from C to XII on the Earth's 
axis G P. So the point XII shall be the place 
of London on the Earth's disc, as seen from the 
Sun, at the instant when it was noon at London 
on the 14th of July 1748. 

Add the Sun's declination 19° 35% to the Lati- 
tude of London 51° 30', and the sum will be 71 
degrees, 5 minutes, for the Sun's distance from 



166 

the vertex of London on the 14th of July at mid- 
night. Therefore, 

From 71° 5', counted upward in the right hand 
side of the semicircle A D B from B to m^ draw 
the right line m n parallel to C Z). Then, taking 
the extent m n in your compasses, set it from C 
towards or beyond P on the Earth's axis C P, as 
it happens to reach short of P or beyond it: but 
in the present case, it reaches so little above P> 
that we may reckon C P to be its whole extent : 
and so, the point P shall represent the place or si- 
tuation of London at midnight, beyond the illu- 
minated part of the Earth's disc, as seen from the 
Sun; and consequently in the dark pait thereof. 

Divide the part of the Earth's axis between XII 
and Pinto two equal parts, XII if and P K: then, 
through the point iT, draw the right line VI KYI 
perpendicular to the Earth's axis C XII R P. 

Substract the Latitude of London, 51° SO', from 
90° CO', and there will remain 38£, for its Co-lati- 
tude. ...Then, from 28°j, counted upward from 
B to v in the semicircle A D J3, draw the right 
line v xv ; and, having taking its length in your 
compasses, set off that length both ways from Kin 
the Earth's axis to VI and VI, in the line VI K VI. 

Nov/, to draw the parallel of Latitude of Lon- 
don, or its path on the Earth's disc, as seen from 
the Sun, from the time of Sun-rise till the time 
of Sun-set at London ; proceed as follows. 

The compasses being opened from K to VI, 
set one foot in K, and with the other foot describe 



167 

the semi-circle VI 7 8 9 10 11 12 i 2 3 4 5 VI. 
and divide it into twelve equal parts. Then, from 
the division points (7 8 9, &c.) draw the right 
lines 7 £, 8 b H 9 c, 10 </, &c. all parallel to the 
Earth's axis C P, as in the figure. 

Set one foot of of the compasses in K, and with 
the other foot describe the semi-circle P L XII, 
and divide its quadrant XII L into six equal parts 
as at the points 1, 2, 3, 4, 5, 6 ; because the Sun 
is on the North side of the Equator. If he had 
been on the South side of it, the quadrant P L 
(and not the quadrant XII i) must have been so 
divided. 

Through the said division-points of the quad* 
rant XII Z, draw the right lines XI 1 I, 2 II, 
IX 3 III, VIII 4 IV, and VII 5 V, all parallel to 
the right line VI K VI ; and through the points 
where these lines meet the former parallel lines 7 
a, 8^9 c, 10 d, &c. draw the elliptical curve VI 
x VII VIII IX X XI XII I II III IV V VI; 
which may be done by hand, from point to point * 
and set the hour-letters to those points where the 
right lines meet in the curve, as in the figure. 
This curve shall represent the parallel of Latitude 
of London, or, the path which London (by the 
Earth's motion on its axis) appear to describe on 
the Earth's disc, as seen from the Sun on the 
14th of July, from VI in the morning till VI at 
night : and the points VI, VII, VIII, IX, &c. in 
the curve shall be the points of the disc where 
London would be at each of these hours respec* 



168 

lively, as seen from the Sun. If the Sun's de- 
clination had been as far South as it was North, 
the dotted curve VI P 31 VI would have been 
the path of London; w T hich must have been found 
by dividing the quadrant P L, into six equal parts, 
and drawing lines parallel to VI K VI between 
that line and the pole P, and continuing the lines 
7 a, 8 b, 9 c, &c. till they met the foresaid parallel 
lines drawn through the division-points of the 

quadrant PL The points/? and G, where the 

elliptical curve touch the circumference of the disc, 
denote the instants of the Sun's rising and setting 
at London; for, when London is at p, it will be 
just entering into the enlightened part of the 
Earth ; and going into the dark, when it is at G. 

From the point 31, viz* 5 degrees, 35 minutes, 
to the right hand of the axis of the Ecliptic C D, 
draw the right line 31 C for the axis of the Moon's 
orbit as seen from the Sun, because the Moon's 
Latitude is North descending, on the 14th of July 
1 748. .♦. If her Latitude had been North ascending, 
the axis of her orbit must have been drawn 5 de* 
grees, 35 minutes, on the left hand side of the 
axis of the Ecliptic. 

Take the Moon's Latitude, 28° 6", from Ctos 
with your compasses, in the scale A C\ and set that 
extent from C to q on the axis (C D) of the 
Ecliptic. Then through the point q, draw the 
right line N q t, perpendicular to the axis of the 
Moon's orbit C z 31; and N qO t shall be the path 
of the center of the Moon's shadow over the 



169 

Earth ; and will represent as much of the Moon's 
orbit, seen from the Sun, as she moves through, 
during the time that her shadow or penumbra is 
going over the Earth. 

From C, on the scale A C, take the Moon's hor- 
ary motion from the Sun, 27' 17", in your compas- 
ses ; and make the line A B (Fig. 2.) equal in 
length to that extent: and divide the said line in- 
to 60 equal parts, for so many minutes of time. 
Then, as the time of new Moon, on the 14th of 
July, 1748, was at 15 minutes, C seconds, after XI 
o'clock, take 15 minutes (neglecting the three se- 
conds) from A to a on the line A B in your com- 
passes, and set them off, in Fig. 1. from the mid- 
dle point between q and z, in the right line N q 
Z 0, to XI in that line ; because the tabular time 
of new Moon is mid-way between the point q y 
tvhere the axis C D of the Ecliptic and the axis 
C M of the Moon's orbit cuts the line or path of 
the penumbra's center on the Earth. 

Take the whole length of the line A B (Fig. 2.) 
in your compasses ; and, with that extent, make 
marks along the line NO (Fig. 1.) both ways from 
XI ; and set the hour-letters to these marks, as in 
the figure. Then divide each space, from mark 
to mark, into sixty equal parts or horary minutes, 
which shall shew the points of the Earth's disc 
where the center of the penumbra falls, at every 
hour and minute, during its transit over the Earth. 

Apply one side of a square to the line of the 
penumbra's path iVO, and move the square for- 



170 

ward or backward till the other side cuts the same 
hour and minute, as at $ and r, both in the path 
of the penumbra's centre and the path of Lon- 
don : and the minute, which the square cuts at the 
same instant in both these paths, is the instant of 
the visible conjunction of the Sun and Moon at 
London ; and consequently, of the greatest obscu- 
ration of the Sun by the Moon; which, according 
to the projection, is at 30 minutes past X o'clock 
in the morning* 

Take the Sun's semldiametef, 15' 50", in your 
compasses from the scale ; and setting one foot at 
r as a centre in the path of London ; with the other 
foot describe the circle R S for the Sun, as seen 
from London at the time of greatest obscuration. 
Then, take the Moon's semidiameter, 14' 53", in 
your compasses from the scale ; and setting one 
foot in the Moon's path at s, with the other foot 
describe the circle 777 for the moon, as seen from 
London, when she obscures most of all of the Sun^ 
during the eclipse : which may be measured by a 
diameter line us r x drawn across the Sun through 
the points 5 and r, and divided into 12 equal parts 
for digits of the Sun's diameter; of which, accord- 
ing- to the present projection, there are 9f digits 
eclipsed. 

Take the semidiameter of the penumbra, 30' 43" 
from the scale in your compasses ; and setting one 
foot in the path of the penumbra's centre, direct 
the other foot to the path of London among the 
morning hours at the left hand ; and carry that 



m 

extent backwards and forwards, till both the points 
of the compasses fall into the same instant in both 
the paths ; which instant will denote the time when 
the eclipse began at London. Then, do the like 
among the afternoon hours ; and where the points 
of the compasses fall into the same instants in both 
the paths, they will shew at what time the eclipse 
ended at London.. ..These trials shew that the be- 
ginning of the eclipse was just at IX oclock in the 
morning, and its ending at 7 minutes after XII 
o'clock at noon ; as the compasses reach just from 
IX in the path of London to IX in the path of the 
penumbra's center ; and from 7 minutes after XII 
in the path of London, to 7 minutes after XII in 
the path of the penumbra's center. Thus, we have, 
at last, finished the projection, and found what was 
wanted to be known from it. 

E. The whole process is very pleasant, but, I 
think, it is somewhat tedious. 

N. That is, because we have been obliged to di- 
vide the semicircle A B D and the quadrant L H 
with a pair of compasses. ...If the Sector had been 
used, the labour would have been much shorten- 
ed, because we could have taken off all the mea- 
sures directly from it ; and so have avoided all 
the trouble of dividing, not only of the semicircle 
and quadrant, but also even of the scale. 

E. I wish you would teach me how to use the 
Sector. 

N% I will send to my mathematical instrument 
maker, Mr. Bennet, in Crown-Court, near Saint 



172 

Ann's Church, Soho, for a complete case of ma- 
thematical instruments, and will make you a pre- 
sent of it, and instruct you how to use them be- 
fore I leave this place. In the mean time r I will 
ask you afew questions relative to the subjects we 
have been upon; and, if you can answer them 
cleverly, I shall not scruple to tell you, that you 
have made a very extraordinary progress. 

£. I thank you, Sir, for your intended present 
and future instructions : and will answer your 
questions as well as I can.^ 

N. What would be the consequence, if the Earth 
were fixed in any point of its orbit, so as to have 
no progressive motion therein ; and to turn round 
its axis with its present velocity, having its axis 
perpendicular to the plane of the Ecliptic ? 

£. The solar, or natural day would be of the 
same length with the sydereal day ; which is equal 
to 23 hours, 56 minutes, 4 seconds, of the time 
now measured by a well regulated clock. The 
Sun would constantly appear to revolve in the 
Equator, days and nights would always be of an 
equal length at all places, either near the poles or 
far from them. And consequently, there would 
be no different seasons. 

N, What would be the consequence, if the 
Moon's distance from the Earth was such, as that 

* The subject of what is here put down, by way of ques- 
tion and answer, was given by the author some time ago 
to a gentleman who has unce published it, not without 
the author's leave, at the end of a printed book. 



173 

she should appear to be of the same magnitude 
with the Sun ; that her orbit were circular, and 
lay in the plane of the ecliptic ; and that she moved 
round the Earth in her orbit with her present ve- 
locity ? 

E. The Moon would always revolve in the plane 
of the Equator ; and (supposing the Earth had no 
progressive motion in its orbit) the Moon would 
go round from change to change in the time she 
now goes round her orbit, which is, in 27 days, 7 
hours, 43 minutes, 5 seconds. The diameters of 
the Sun and Moon would always appear to be 
equal. The Moon would eclipse the Sun totally, 
for an instant of time, at all those places over 
which the center of her shadow passed, which 
would be directly along the Equator. The eclip- 
ses would be only partial on different sides of the 
Equator, and never visible at more than 235C 
miles from it. The Moon would be totally 
eclipsed in the Earth's shadow at every time she 
was full ; and the durations of all her eclipses 
would be equal. 

JV. What would be the consequence, if the 
Moon's orbit acquired an elliptical form, such as 
it is now of : that it continued in the plane of the 
ecliptic, and the Earth had no progressive mo- 
tion, but only turned round its axis as before? 

E. The lengths of days and nights would be 
the same as above, and the times between the new 
or full Moons would remain the same. The Sua 
would be eclipsed (as above) at every change, and 

p 2 



1H 

the Moon at every full ; and the center of the 
Moon's shadow, when the Moon is new, would 
always pass along the Equator. If the changes fell 
in that part of the Moon's orbit which is farthest 
from the Earth, the Sun would never be totally 
eclipsed ; but would appear like a fine luminous 
ring all around the dark body of the Moon, at 
these places on the Equator where the Moon were 
directly over head at the instant of the change. 
If the changes fell in that part of the Moon's or- 
bit which is nearest the Earth, all the eclipses of 
the Sun would be total at the Equator, for about 
four minutes of time : but if they fell in either of 
the two parts of the Moon's orbit, which are fit a 
mean between those parts which are at the great- 
est and least distance from the Earth, the eclipses 
of tne Sun would be just total for an instant of time 
at the Equator, and no where else. All the Moon's 
eclipses would be total with continuance as above.. 

JV. Suppose now, that the Earth should revolve 
about the Sun, with its present velocity, in the plane 
of the ecliptic, its axis keeping always perpendicuv 
lar thereto: that the Moon should revolve as above 
with her present velocity; and that her orbit should 
remain always in the plane of the ecliptic. 

£. In that case, the days and nights would al- 
way continue (as above) of equal length ; only the 
24 solar hours would be 3 minutes, 56 seconds, 
longer than the 24 sydereal hours, as they now 
are ; but there would be no different seasons. 
The JNIoon would go round her orbit in 27 days,, 



1T5 

7 hours 43 minutes, 5 seconds ; and round from 
the Sun to the Sun again, or from change to 
change, in 29 days, 12 hours, 44 minutes, three 
seconds ; as she now does. The Sun would be 
eclipsed (as above) at every change, and the Moon 
at every full ; and all the Sun's eclipses would be 
central only at the Equator ; but they would some- 
times be total there for four minutes, sometimes 
total only for an instant, and at other times an- 
nular, according to the distance of the Moon 
from the Earth in different parts of her elliptical 
orbit at these times. 

N. With the above circumstances, relating to 
the Earth's progressive motion in its orbit, and 
the Moon's motion in her orbit; what would be 
the consequence if the Earth's axis should become 
inclined to the ecliptic, as it now is ; and the 
Earth turn round its axis with its present velocity ? 

E* We should have all the varietv of seasons 
we now enjoy. The times between the new and 
full Moons would be the same as in the last an- 
swer above, and the eclipses of the Sun and Moon 
the same. Only, the Sun's central eclipses would 
not fall always at the Equator, but sometimes on 
one side of it, and sometimes on the other ; that 
is, between the Equator and that pole of the Earth 
which was inclining toward the Sun at the time 
of the eclipse*.. ..In our spring, the center of the 
Moon's shadow would go obliquely over the 
Earth, from the southern tropic to the northern. 
In summer, the shadow would begin to take the 



ire 

Earth at the Equator, and thence bend its course 
to the northern tropic, and from that tropic to 
the Equator again, where it would leave the 
Earth. In our autumn, the center of the Moon's 
shadow would go obliquely over the Earth, from 
the northern tropic to the southern :....and, in 
winter, it would take the Earth at the Equator, 
from which it would bend its course to the southern 
tropic, and go on obliquely from that tropic to the 
Equator, where it would leave the Earth. And, 
in each of these four cases, the Sun's eclipses 
would be central to all the parts of the Earth over 
which the center of the Moon's shadow passed ; 
sometimes total only for an instant, sometimes total 
for four minutes, and at other times only annular 
• ...The eclipses of the Moon would be as above. 

iV. Supposing now that the Moon's orbit should 
become inclined to the Ecliptic, as it is at pre- 
sent, but that her nodes should have no motion 
therein ; and every other circumstance should 
remain as in the last question ? 

E. Then, the Sun, would never be eclipsed at 
more than 17 degrees from either of the nodes, at 
the time of any new Moon whatever ; nor would 
the Moon be eclipsed at more than 12 degrees 
from either of the nodes at any time whatever of 
being full. So that we should have but few eclip- 
ses (as is now the case) in comparison of the ^um- 
ber of our new and full Moons. And the eclipses 
would be confined to the same seasons of the 
year \ for there would be half a year between 



m 

those which happened about one node and -about 
the other, because there would be just half a year 
between the conjunctions of the Sun with one 
node and with the other. 

iV. Every thing remaining as above, excepting 
the stability of the nodes, and of those two points 
of the Moon's orbit which are most and least dis- 
tant from the Earth : what would be the conse- 
quence if these points acquired a direct or for- 
ward motion in the Moon's orbit, and her nodes 
a backward or retrograde motion ; as they now 
have ? 

E. I believe, every circumstance would be as 
it now is ; and therefore we should have all the 
variety of eclipses that now exists in nature. 

N. Well done, Eudosia !....You have answered 
all my questions to my mind : which you could 
not possibly have done, unless you had very well 
remembered the subjects we have been upon, in 
all our Ten Dialogues. This, I think, may be 
our last on Astronomy ; because your applying to 
books will supersede all necessity of our having 
any more. 

E. But I am extremely sorry, brother, to have 
heard yesterday, that you are to set out for Italy 
in a few days, which is much sooner than was ex- 
pected. I shall miss you sadly ;....and as you will 
probably be gone before I can read Fergusons 
Astronomy quite through, I should be glad to 
know whether you would have me to read any 
other book upon the like subject afterward* 



m 

JV. *By all means..,. ..Here is Doctor Long's 
Astronomy ; take it and keep it ; for it will afford 
you a great deal of entertaining and pleasing 
knowledge, especially in the historical part.... You 
may skip over those parts which are geometrical, 
as I shall not now have time to instruct you in 
that branch of science* It is true the volume is 
large, but I will answer for it, that by the time you 
have got to the end, you will wish it had been 
much larger, and that the Doctor would finish 
his second volume. 

JE. Permit me, dear brother, to thank you most 
sincerely for this valuable present. 



THE END. 



DIRECTIONS TO THE BINDER. 

All the Plates are to be opened toward the L 
Hand, and to be placed as fellows, 

Plate I. - 

II.- 
III. 
IV. 

V. ... 

VI. 
VII. 



*D 



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